diff --git a/recipes/libxml2/all/conanfile.py b/recipes/libxml2/all/conanfile.py
index 135d4bdbf88af..c183f8d0d6e08 100644
--- a/recipes/libxml2/all/conanfile.py
+++ b/recipes/libxml2/all/conanfile.py
@@ -86,6 +86,9 @@ def configure(self):
         self.settings.rm_safe("compiler.libcxx")
         self.settings.rm_safe("compiler.cppstd")
 
+    def layout(self):
+        basic_layout(self, src_folder="src")
+
     def requirements(self):
         if self.options.zlib:
             self.requires("zlib/1.2.13")
@@ -94,10 +97,7 @@ def requirements(self):
         if self.options.iconv:
             self.requires("libiconv/1.17")
         if self.options.icu:
-            self.requires("icu/71.1")
-
-    def layout(self):
-        basic_layout(self, src_folder="src")
+            self.requires("icu/72.1")
 
     def build_requirements(self):
         if not (is_msvc(self) or self._is_mingw_windows):
@@ -151,7 +151,6 @@ def generate(self):
             tc = AutotoolsDeps(self)
             tc.generate()
 
-
     def _build_msvc(self):
         with chdir(self, os.path.join(self.source_folder, 'win32')):
             debug = "yes" if self.settings.build_type == "Debug" else "no"
@@ -215,7 +214,6 @@ def _package_msvc(self):
             if self.options.include_utils:
                 self.run("nmake /f Makefile.msvc install-dist")
 
-
     def _build_mingw(self):
         with chdir(self, os.path.join(self.source_folder, "win32")):
             # configuration
@@ -269,7 +267,6 @@ def _package_mingw(self):
             if self.options.include_utils:
                 self.run("mingw32-make -f Makefile.mingw install-dist")
 
-
     def _patch_sources(self):
         # Break dependency of install on build
         for makefile in ("Makefile.mingw", "Makefile.msvc"):
@@ -281,7 +278,6 @@ def _patch_sources(self):
                               "-install_name \\$rpath/",
                               "-install_name @rpath/")
 
-
     def build(self):
         self._patch_sources()
         if is_msvc(self):
@@ -345,22 +341,31 @@ def package(self):
     def _create_cmake_module_variables(self, module_file):
         # FIXME: also define LIBXML2_XMLLINT_EXECUTABLE variable
         content = textwrap.dedent("""\
-            if(DEFINED LibXml2_FOUND)
-                set(LIBXML2_FOUND ${LibXml2_FOUND})
-            endif()
-            if(DEFINED LibXml2_INCLUDE_DIR)
-                set(LIBXML2_INCLUDE_DIR ${LibXml2_INCLUDE_DIR})
-                set(LIBXML2_INCLUDE_DIRS ${LibXml2_INCLUDE_DIR})
+            set(LibXml2_FOUND TRUE)
+            set(LIBXML2_FOUND TRUE)
+            if(DEFINED LibXml2_INCLUDE_DIRS)
+                set(LIBXML2_INCLUDE_DIR ${LibXml2_INCLUDE_DIRS})
+                set(LIBXML2_INCLUDE_DIRS ${LibXml2_INCLUDE_DIRS})
+            elseif(DEFINED libxml2_INCLUDE_DIRS)
+                set(LIBXML2_LIBRARIES ${libxml2_INCLUDE_DIRS})
+                set(LIBXML2_LIBRARY ${libxml2_INCLUDE_DIRS})
             endif()
             if(DEFINED LibXml2_LIBRARIES)
                 set(LIBXML2_LIBRARIES ${LibXml2_LIBRARIES})
                 set(LIBXML2_LIBRARY ${LibXml2_LIBRARIES})
+            elseif(DEFINED libxml2_LIBRARIES)
+                set(LIBXML2_LIBRARIES ${libxml2_LIBRARIES})
+                set(LIBXML2_LIBRARY ${libxml2_LIBRARIES})
             endif()
             if(DEFINED LibXml2_DEFINITIONS)
                 set(LIBXML2_DEFINITIONS ${LibXml2_DEFINITIONS})
+            elseif(DEFINED libxml2_DEFINITIONS)
+                set(LIBXML2_DEFINITIONS ${libxml2_DEFINITIONS})
             endif()
             if(DEFINED LibXml2_VERSION)
                 set(LIBXML2_VERSION_STRING ${LibXml2_VERSION})
+            elseif(DEFINED libxml2_VERSION)
+                set(LIBXML2_VERSION_STRING ${libxml2_VERSION})
             endif()
         """)
         save(self, module_file, content)
diff --git a/recipes/libxml2/all/test_cmake_module_package/CMakeLists.txt b/recipes/libxml2/all/test_cmake_module_package/CMakeLists.txt
deleted file mode 100644
index 39f1f2e09e014..0000000000000
--- a/recipes/libxml2/all/test_cmake_module_package/CMakeLists.txt
+++ /dev/null
@@ -1,15 +0,0 @@
-cmake_minimum_required(VERSION 3.8)
-project(test_package C)
-
-find_package(LibXml2 REQUIRED)
-
-message("LIBXML2_FOUND: ${LIBXML2_FOUND}")
-message("LIBXML2_INCLUDE_DIR: ${LIBXML2_INCLUDE_DIR}")
-message("LIBXML2_INCLUDE_DIRS: ${LIBXML2_INCLUDE_DIRS}")
-message("LIBXML2_LIBRARIES: ${LIBXML2_LIBRARIES}")
-message("LIBXML2_LIBRARY: ${LIBXML2_LIBRARY}")
-message("LIBXML2_DEFINITIONS: ${LIBXML2_DEFINITIONS}")
-message("LIBXML2_VERSION_STRING: ${LIBXML2_VERSION_STRING}")
-
-add_executable(${PROJECT_NAME} ../test_package/test_package.c)
-target_link_libraries(${PROJECT_NAME} LibXml2::LibXml2)
diff --git a/recipes/libxml2/all/test_module_package/CMakeLists.txt b/recipes/libxml2/all/test_module_package/CMakeLists.txt
new file mode 100644
index 0000000000000..90d37ee9afb23
--- /dev/null
+++ b/recipes/libxml2/all/test_module_package/CMakeLists.txt
@@ -0,0 +1,26 @@
+cmake_minimum_required(VERSION 3.12)
+project(test_package LANGUAGES C)
+
+find_package(LibXml2 REQUIRED MODULE)
+
+add_executable(${PROJECT_NAME} ../test_package/test_package.c)
+target_link_libraries(${PROJECT_NAME} PRIVATE LibXml2::LibXml2)
+
+# Test whether variables from https://cmake.org/cmake/help/latest/module/FindLibXml2.html
+# are properly defined in conan generators
+set(_custom_vars
+    LibXml2_FOUND # since CMake 3.14
+    LIBXML2_FOUND # until CMake 3.14
+    LIBXML2_INCLUDE_DIR
+    LIBXML2_INCLUDE_DIRS
+    LIBXML2_LIBRARIES
+    LIBXML2_DEFINITIONS
+    LIBXML2_VERSION_STRING
+)
+foreach(_custom_var ${_custom_vars})
+    if(DEFINED _custom_var)
+        message(STATUS "${_custom_var}: ${${_custom_var}}")
+    else()
+        message(FATAL_ERROR "${_custom_var} not defined")
+    endif()
+endforeach()
diff --git a/recipes/libxml2/all/test_cmake_module_package/conanfile.py b/recipes/libxml2/all/test_module_package/conanfile.py
similarity index 88%
rename from recipes/libxml2/all/test_cmake_module_package/conanfile.py
rename to recipes/libxml2/all/test_module_package/conanfile.py
index 3eab19928545d..20481a742d614 100644
--- a/recipes/libxml2/all/test_cmake_module_package/conanfile.py
+++ b/recipes/libxml2/all/test_module_package/conanfile.py
@@ -23,5 +23,5 @@ def build(self):
     def test(self):
         if can_run(self):
             bin_path = os.path.join(self.cpp.build.bindirs[0], "test_package")
-            xml_path = os.path.join(self.source_folder, "..", "test_package", "books.xml")
+            xml_path = os.path.join(self.source_folder, os.pardir, "test_package", "books.xml")
             self.run(f"{bin_path} {xml_path}", env="conanrun")
diff --git a/recipes/libxml2/all/test_package/CMakeLists.txt b/recipes/libxml2/all/test_package/CMakeLists.txt
index 60662e900b4c8..9d8bc300051af 100644
--- a/recipes/libxml2/all/test_package/CMakeLists.txt
+++ b/recipes/libxml2/all/test_package/CMakeLists.txt
@@ -1,7 +1,7 @@
 cmake_minimum_required(VERSION 3.1)
-project(test_package C)
+project(test_package LANGUAGES C)
 
-find_package(libxml2 CONFIG REQUIRED)
+find_package(libxml2 REQUIRED CONFIG)
 
 add_executable(${PROJECT_NAME} test_package.c)
-target_link_libraries(${PROJECT_NAME} LibXml2::LibXml2)
+target_link_libraries(${PROJECT_NAME} PRIVATE LibXml2::LibXml2)
diff --git a/recipes/libxml2/all/test_v1_cmake_module_package/CMakeLists.txt b/recipes/libxml2/all/test_v1_cmake_module_package/CMakeLists.txt
deleted file mode 100644
index 487747f324c50..0000000000000
--- a/recipes/libxml2/all/test_v1_cmake_module_package/CMakeLists.txt
+++ /dev/null
@@ -1,18 +0,0 @@
-cmake_minimum_required(VERSION 3.1)
-project(test_package C)
-
-include(${CMAKE_BINARY_DIR}/conanbuildinfo.cmake)
-conan_basic_setup(TARGETS)
-
-find_package(LibXml2 REQUIRED)
-
-message("LIBXML2_FOUND: ${LIBXML2_FOUND}")
-message("LIBXML2_INCLUDE_DIR: ${LIBXML2_INCLUDE_DIR}")
-message("LIBXML2_INCLUDE_DIRS: ${LIBXML2_INCLUDE_DIRS}")
-message("LIBXML2_LIBRARIES: ${LIBXML2_LIBRARIES}")
-message("LIBXML2_LIBRARY: ${LIBXML2_LIBRARY}")
-message("LIBXML2_DEFINITIONS: ${LIBXML2_DEFINITIONS}")
-message("LIBXML2_VERSION_STRING: ${LIBXML2_VERSION_STRING}")
-
-add_executable(${PROJECT_NAME} ../test_package/test_package.c)
-target_link_libraries(${PROJECT_NAME} LibXml2::LibXml2)
diff --git a/recipes/libxml2/all/test_v1_module_package/CMakeLists.txt b/recipes/libxml2/all/test_v1_module_package/CMakeLists.txt
new file mode 100644
index 0000000000000..75233d23b3349
--- /dev/null
+++ b/recipes/libxml2/all/test_v1_module_package/CMakeLists.txt
@@ -0,0 +1,8 @@
+cmake_minimum_required(VERSION 3.1)
+project(test_package)
+
+include(${CMAKE_BINARY_DIR}/conanbuildinfo.cmake)
+conan_basic_setup(TARGETS)
+
+add_subdirectory(${CMAKE_CURRENT_SOURCE_DIR}/../test_module_package
+                 ${CMAKE_CURRENT_BINARY_DIR}/test_module_package)
diff --git a/recipes/libxml2/all/test_v1_cmake_module_package/conanfile.py b/recipes/libxml2/all/test_v1_module_package/conanfile.py
similarity index 66%
rename from recipes/libxml2/all/test_v1_cmake_module_package/conanfile.py
rename to recipes/libxml2/all/test_v1_module_package/conanfile.py
index 3bec0de0bab22..ca3b4e232a4f3 100644
--- a/recipes/libxml2/all/test_v1_cmake_module_package/conanfile.py
+++ b/recipes/libxml2/all/test_v1_module_package/conanfile.py
@@ -14,6 +14,5 @@ def build(self):
     def test(self):
         if not tools.cross_building(self):
             bin_path = os.path.join("bin", "test_package")
-            xml_path = os.path.join(self.source_folder, "..", "test_package", "books.xml")
-            bin_arg_path = "%s %s" % (bin_path, xml_path)
-            self.run(bin_arg_path, run_environment=True)
+            xml_path = os.path.join(self.source_folder, os.pardir, "test_package", "books.xml")
+            self.run(f"{bin_path} {xml_path}", run_environment=True)
diff --git a/recipes/libxml2/all/test_v1_package/CMakeLists.txt b/recipes/libxml2/all/test_v1_package/CMakeLists.txt
index ea045cdb5efca..0d20897301b68 100644
--- a/recipes/libxml2/all/test_v1_package/CMakeLists.txt
+++ b/recipes/libxml2/all/test_v1_package/CMakeLists.txt
@@ -1,17 +1,8 @@
 cmake_minimum_required(VERSION 3.1)
-project(test_package C)
+project(test_package)
 
 include(${CMAKE_BINARY_DIR}/conanbuildinfo.cmake)
 conan_basic_setup(TARGETS)
 
-find_package(LibXml2 REQUIRED)
-message("LIBXML2_FOUND: ${LIBXML2_FOUND}")
-message("LIBXML2_INCLUDE_DIR: ${LIBXML2_INCLUDE_DIR}")
-message("LIBXML2_INCLUDE_DIRS: ${LIBXML2_INCLUDE_DIRS}")
-message("LIBXML2_LIBRARIES: ${LIBXML2_LIBRARIES}")
-message("LIBXML2_LIBRARY: ${LIBXML2_LIBRARY}")
-message("LIBXML2_DEFINITIONS: ${LIBXML2_DEFINITIONS}")
-message("LIBXML2_VERSION_STRING: ${LIBXML2_VERSION_STRING}")
-
-add_executable(${PROJECT_NAME} ../test_package/test_package.c)
-target_link_libraries(${PROJECT_NAME} LibXml2::LibXml2)
+add_subdirectory(${CMAKE_CURRENT_SOURCE_DIR}/../test_package
+                 ${CMAKE_CURRENT_BINARY_DIR}/test_package)
diff --git a/recipes/libxml2/all/test_v1_package/conanfile.py b/recipes/libxml2/all/test_v1_package/conanfile.py
index 3bec0de0bab22..ae0f76f08489b 100644
--- a/recipes/libxml2/all/test_v1_package/conanfile.py
+++ b/recipes/libxml2/all/test_v1_package/conanfile.py
@@ -3,8 +3,8 @@
 
 
 class TestPackageConan(ConanFile):
-    settings = "os", "compiler", "build_type", "arch"
-    generators = "cmake", "cmake_find_package"
+    settings = "os", "arch", "compiler", "build_type"
+    generators = "cmake", "cmake_find_package_multi"
 
     def build(self):
         cmake = CMake(self)
@@ -14,6 +14,5 @@ def build(self):
     def test(self):
         if not tools.cross_building(self):
             bin_path = os.path.join("bin", "test_package")
-            xml_path = os.path.join(self.source_folder, "..", "test_package", "books.xml")
-            bin_arg_path = "%s %s" % (bin_path, xml_path)
-            self.run(bin_arg_path, run_environment=True)
+            xml_path = os.path.join(self.source_folder, os.pardir, "test_package", "books.xml")
+            self.run(f"{bin_path} {xml_path}", run_environment=True)