diff --git a/packages/pyright-internal/src/analyzer/typeEvaluator.ts b/packages/pyright-internal/src/analyzer/typeEvaluator.ts
index e0971032b..00549d926 100644
--- a/packages/pyright-internal/src/analyzer/typeEvaluator.ts
+++ b/packages/pyright-internal/src/analyzer/typeEvaluator.ts
@@ -19130,6 +19130,20 @@ export function createTypeEvaluator(importLookup: ImportLookup, evaluatorOptions
             }
         }
 
+        // Handle the special case where the dest is a union of Any and
+        // a type variable and CanAssignFlags.AllowTypeVarNarrowing is
+        // in effect. This occurs, for example, with the return type of
+        // the getattr function.
+        if ((flags & CanAssignFlags.AllowTypeVarNarrowing) !== 0 && isUnion(destType)) {
+            const nonAnySubtypes = destType.subtypes.filter((t) => !isAnyOrUnknown(t));
+            if (nonAnySubtypes.length === 1 && isTypeVar(nonAnySubtypes[0])) {
+                canAssignType(nonAnySubtypes[0], srcType, /* diag */ undefined, typeVarMap, flags, recursionCount + 1);
+
+                // This always succeeds because the destination contains Any.
+                return true;
+            }
+        }
+
         // For union sources, all of the types need to be assignable to the dest.
         let isIncompatible = false;
         doForEachSubtype(srcType, (subtype) => {
diff --git a/packages/pyright-internal/src/tests/samples/genericTypes72.py b/packages/pyright-internal/src/tests/samples/genericTypes72.py
new file mode 100644
index 000000000..4cbe80a46
--- /dev/null
+++ b/packages/pyright-internal/src/tests/samples/genericTypes72.py
@@ -0,0 +1,15 @@
+# This sample tests a special case of bidirectional type inference when
+# the expected type is a union and the destination type is a union that
+# contains Any and a TypeVar.
+
+
+from typing import Any, Literal, TypeVar
+
+_T = TypeVar("_T")
+
+
+def getattr(__o: object, name: str, __default: _T) -> Any | _T:
+    ...
+
+
+x: Literal[1, 2, 3] = getattr(object(), "", 1)
diff --git a/packages/pyright-internal/src/tests/typeEvaluator2.test.ts b/packages/pyright-internal/src/tests/typeEvaluator2.test.ts
index b1c4064bb..83c70c3de 100644
--- a/packages/pyright-internal/src/tests/typeEvaluator2.test.ts
+++ b/packages/pyright-internal/src/tests/typeEvaluator2.test.ts
@@ -757,6 +757,12 @@ test('GenericTypes71', () => {
     TestUtils.validateResults(analysisResults, 4);
 });
 
+test('GenericTypes72', () => {
+    const analysisResults = TestUtils.typeAnalyzeSampleFiles(['genericTypes72.py']);
+
+    TestUtils.validateResults(analysisResults, 0);
+});
+
 test('Protocol1', () => {
     const analysisResults = TestUtils.typeAnalyzeSampleFiles(['protocol1.py']);