diff --git a/compiler/src/dotty/tools/dotc/typer/Checking.scala b/compiler/src/dotty/tools/dotc/typer/Checking.scala
index e3b35e6b7f73..7629776525a0 100644
--- a/compiler/src/dotty/tools/dotc/typer/Checking.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Checking.scala
@@ -721,12 +721,6 @@ object Checking {
           else "Cannot override non-inline parameter with an inline parameter",
           p1.srcPos)
 
-  def checkConversionsSpecific(to: Type, pos: SrcPos)(using Context): Unit =
-    if to.isRef(defn.AnyValClass, skipRefined = false)
-       || to.isRef(defn.ObjectClass, skipRefined = false)
-    then
-      report.error(em"the result of an implicit conversion must be more specific than $to", pos)
-
   def checkValue(tree: Tree)(using Context): Unit =
     val sym = tree.tpe.termSymbol
     if sym.isNoValue && !ctx.isJava then
diff --git a/compiler/src/dotty/tools/dotc/typer/Implicits.scala b/compiler/src/dotty/tools/dotc/typer/Implicits.scala
index 9a42babcd38e..e8e49071bf2b 100644
--- a/compiler/src/dotty/tools/dotc/typer/Implicits.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Implicits.scala
@@ -503,6 +503,14 @@ object Implicits:
   @sharable val ImplicitSearchTooLargeFailure: SearchFailure =
     SearchFailure(ImplicitSearchTooLarge, NoSpan)(using NoContext)
 
+  /** A failure value indicating that an implicit search for a conversion was not tried */
+  class TooUnspecific(target: Type) extends NoMatchingImplicits(NoType, EmptyTree, OrderingConstraint.empty):
+    override def whyNoConversion(using Context): String =
+      i"""
+         |Note that implicit conversions were not tried because the result of an implicit conversion
+         |must be more specific than $target"""
+    override def toString = s"TooUnspecific"
+
   /** An ambiguous implicits failure */
   class AmbiguousImplicits(val alt1: SearchSuccess, val alt2: SearchSuccess, val expectedType: Type, val argument: Tree) extends SearchFailureType {
     def explanation(using Context): String =
diff --git a/compiler/src/dotty/tools/dotc/typer/Typer.scala b/compiler/src/dotty/tools/dotc/typer/Typer.scala
index 06dc361b9952..2fac5f25d668 100644
--- a/compiler/src/dotty/tools/dotc/typer/Typer.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Typer.scala
@@ -3980,8 +3980,11 @@ class Typer(@constructorOnly nestingLevel: Int = 0) extends Namer
               case None => tree
           else tree // other adaptations for selections are handled in typedSelect
         case _ if ctx.mode.is(Mode.ImplicitsEnabled) && tree.tpe.isValueType =>
-          checkConversionsSpecific(pt, tree.srcPos)
-          inferView(tree, pt) match
+          if pt.isRef(defn.AnyValClass, skipRefined = false)
+              || pt.isRef(defn.ObjectClass, skipRefined = false)
+          then
+            recover(TooUnspecific(pt))
+          else inferView(tree, pt) match
             case SearchSuccess(found, _, _, isExtension) =>
               if isExtension then found
               else
diff --git a/tests/neg/i6336.check b/tests/neg/i6336.check
new file mode 100644
index 000000000000..a4afb885ec98
--- /dev/null
+++ b/tests/neg/i6336.check
@@ -0,0 +1,18 @@
+-- [E007] Type Mismatch Error: tests/neg/i6336.scala:2:18 --------------------------------------------------------------
+2 |  val a: AnyVal = "foo" // error
+  |                  ^^^^^
+  |                  Found:    ("foo" : String)
+  |                  Required: AnyVal
+  |                  Note that implicit conversions were not tried because the result of an implicit conversion
+  |                  must be more specific than AnyVal
+  |
+  | longer explanation available when compiling with `-explain`
+-- [E007] Type Mismatch Error: tests/neg/i6336.scala:3:18 --------------------------------------------------------------
+3 |  val b: AnyRef = 1 // error
+  |                  ^
+  |                  Found:    (1 : Int)
+  |                  Required: AnyRef
+  |                  Note that implicit conversions were not tried because the result of an implicit conversion
+  |                  must be more specific than AnyRef
+  |
+  | longer explanation available when compiling with `-explain`