diff --git a/src/compiler/checker.ts b/src/compiler/checker.ts
index e80be0bfe45..722c223a842 100644
--- a/src/compiler/checker.ts
+++ b/src/compiler/checker.ts
@@ -9927,9 +9927,9 @@ namespace ts {
             }
 
             const apparentType = getApparentType(getWidenedType(type));
-            if (apparentType === unknownType) {
-                // handle cases when type is Type parameter with invalid constraint
-                return unknownType;
+            if (apparentType === unknownType || (type.flags & TypeFlags.TypeParameter && isTypeAny(apparentType))) {
+                // handle cases when type is Type parameter with invalid or any constraint
+                return apparentType;
             }
             const prop = getPropertyOfType(apparentType, right.text);
             if (!prop) {
@@ -11120,7 +11120,9 @@ namespace ts {
             // types are provided for the argument expressions, and the result is always of type Any.
             // We exclude union types because we may have a union of function types that happen to have
             // no common signatures.
-            if (isTypeAny(funcType) || (!callSignatures.length && !constructSignatures.length && !(funcType.flags & TypeFlags.Union) && isTypeAssignableTo(funcType, globalFunctionType))) {
+            if (isTypeAny(funcType) ||
+                (isTypeAny(apparentType) && funcType.flags & TypeFlags.TypeParameter) ||
+                (!callSignatures.length && !constructSignatures.length && !(funcType.flags & TypeFlags.Union) && isTypeAssignableTo(funcType, globalFunctionType))) {
                 // The unknownType indicates that an error already occurred (and was reported).  No
                 // need to report another error in this case.
                 if (funcType !== unknownType && node.typeArguments) {