diff --git a/compiler/src/dotty/tools/dotc/transform/SymUtils.scala b/compiler/src/dotty/tools/dotc/transform/SymUtils.scala
index c7f9c762e440..7694a7cc240a 100644
--- a/compiler/src/dotty/tools/dotc/transform/SymUtils.scala
+++ b/compiler/src/dotty/tools/dotc/transform/SymUtils.scala
@@ -64,6 +64,8 @@ object SymUtils:
 
     def isSuperAccessor(using Context): Boolean = self.name.is(SuperAccessorName)
 
+    def isNoValue(using Context): Boolean = self.is(Package) || self.isAllOf(JavaModule)
+
     /** Is this a type or term parameter or a term parameter accessor? */
     def isParamOrAccessor(using Context): Boolean =
       self.is(Param) || self.is(ParamAccessor)
diff --git a/compiler/src/dotty/tools/dotc/typer/Checking.scala b/compiler/src/dotty/tools/dotc/typer/Checking.scala
index 0525ce805d2e..6e8fa8b9c9d8 100644
--- a/compiler/src/dotty/tools/dotc/typer/Checking.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Checking.scala
@@ -713,7 +713,7 @@ object Checking {
 
   def checkValue(tree: Tree)(using Context): Unit =
     val sym = tree.tpe.termSymbol
-    if sym.is(Flags.Package) || sym.isAllOf(Flags.JavaModule) && !ctx.isJava then
+    if sym.isNoValue && !ctx.isJava then
       report.error(JavaSymbolIsNotAValue(sym), tree.srcPos)
 
   def checkValue(tree: Tree, proto: Type)(using Context): tree.type =
diff --git a/compiler/src/dotty/tools/dotc/typer/Typer.scala b/compiler/src/dotty/tools/dotc/typer/Typer.scala
index a85b2574e59c..ac8d6152812e 100644
--- a/compiler/src/dotty/tools/dotc/typer/Typer.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Typer.scala
@@ -3245,6 +3245,8 @@ class Typer(@constructorOnly nestingLevel: Int = 0) extends Namer
       rememberSearchFailure(qual,
         SearchFailure(qual.withType(NestedFailure(ex.toMessage, selectionProto))))
 
+    if qual.symbol.isNoValue then return EmptyTree
+
     // try an extension method in scope
     try
       val nestedCtx = ctx.fresh.setNewTyperState()
diff --git a/tests/neg/i12537.scala b/tests/neg/i12537.scala
new file mode 100644
index 000000000000..f6c6347bf47e
--- /dev/null
+++ b/tests/neg/i12537.scala
@@ -0,0 +1,2 @@
+extension [T](x: T) def ext: T = x
+def foo = String.ext  // error
diff --git a/tests/neg/i7750.scala b/tests/neg/i7750.scala
index 6b29a6e68640..bdbe3b8f33bc 100644
--- a/tests/neg/i7750.scala
+++ b/tests/neg/i7750.scala
@@ -1,3 +1,3 @@
-package object A extends runtime.A {
+package object A extends runtime.A {  // error
     implicit def a( : ) = 1() // error // error // error
 }
\ No newline at end of file