diff --git a/mypy/checker.py b/mypy/checker.py
index 46c83cdc9c79..39951703c9f8 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -1235,13 +1235,23 @@ def check_func_def(self, defn: FuncItem, typ: CallableType, name: str | None) ->
 
     def check_unbound_return_typevar(self, typ: CallableType) -> None:
         """Fails when the return typevar is not defined in arguments."""
-        if typ.ret_type in typ.variables:
-            arg_type_visitor = CollectArgTypes()
+        if isinstance(typ.ret_type, TypeVarType) and typ.ret_type in typ.variables:
+            arg_type_visitor = CollectArgTypeVarTypes()
             for argtype in typ.arg_types:
                 argtype.accept(arg_type_visitor)
 
             if typ.ret_type not in arg_type_visitor.arg_types:
                 self.fail(message_registry.UNBOUND_TYPEVAR, typ.ret_type, code=TYPE_VAR)
+                upper_bound = get_proper_type(typ.ret_type.upper_bound)
+                if not (
+                    isinstance(upper_bound, Instance)
+                    and upper_bound.type.fullname == "builtins.object"
+                ):
+                    self.note(
+                        "Consider using the upper bound "
+                        f"{format_type(typ.ret_type.upper_bound)} instead",
+                        context=typ.ret_type,
+                    )
 
     def check_default_args(self, item: FuncItem, body_is_trivial: bool) -> None:
         for arg in item.arguments:
@@ -6156,7 +6166,7 @@ class Foo(Enum):
         )
 
 
-class CollectArgTypes(TypeTraverserVisitor):
+class CollectArgTypeVarTypes(TypeTraverserVisitor):
     """Collects the non-nested argument types in a set."""
 
     def __init__(self) -> None:
diff --git a/test-data/unit/check-classes.test b/test-data/unit/check-classes.test
index 8adf2e7ed5f1..45293369dc9b 100644
--- a/test-data/unit/check-classes.test
+++ b/test-data/unit/check-classes.test
@@ -3233,6 +3233,7 @@ def error(u_c: Type[U]) -> P: # Error here, see below
 [out]
 main:11: note: Revealed type is "__main__.WizUser"
 main:12: error: A function returning TypeVar should receive at least one argument containing the same Typevar
+main:12: note: Consider using the upper bound "ProUser" instead
 main:13: error: Value of type variable "P" of "new_pro" cannot be "U"
 main:13: error: Incompatible return value type (got "U", expected "P")
 
diff --git a/test-data/unit/check-typevar-unbound.test b/test-data/unit/check-typevar-unbound.test
index 8761cd94027e..e554e4b514bf 100644
--- a/test-data/unit/check-typevar-unbound.test
+++ b/test-data/unit/check-typevar-unbound.test
@@ -1,4 +1,3 @@
-
 [case testUnboundTypeVar]
 from typing import TypeVar
 
@@ -6,9 +5,19 @@ T = TypeVar('T')
 
 def f() -> T: # E: A function returning TypeVar should receive at least one argument containing the same Typevar
     ...
-
 f()
 
+U = TypeVar('U', bound=int)
+
+def g() -> U: # E: A function returning TypeVar should receive at least one argument containing the same Typevar \
+              # N: Consider using the upper bound "int" instead
+    ...
+
+V = TypeVar('V', int, str)
+
+# TODO: this should also give an error
+def h() -> V:
+    ...
 
 [case testInnerFunctionTypeVar]
 
@@ -21,7 +30,6 @@ def g(a: T) -> T:
         ...
     return f()
 
-
 [case testUnboundIterableOfTypeVars]
 from typing import Iterable, TypeVar
 
@@ -29,7 +37,6 @@ T = TypeVar('T')
 
 def f() -> Iterable[T]:
     ...
-
 f()
 
 [case testBoundTypeVar]
@@ -40,7 +47,6 @@ T = TypeVar('T')
 def f(a: T, b: T, c: int) -> T:
     ...
 
-
 [case testNestedBoundTypeVar]
 from typing import Callable, List, Union, Tuple, TypeVar