diff --git a/tests/tests_pytorch/test_cli.py b/tests/tests_pytorch/test_cli.py
index f60eadbf38898..de89d094cdfcf 100644
--- a/tests/tests_pytorch/test_cli.py
+++ b/tests/tests_pytorch/test_cli.py
@@ -754,6 +754,7 @@ def add_arguments_to_parser(self, parser):
 
 
 @_xfail_python_ge_3_11_9
+@RunIf(min_torch="2.2")
 @pytest.mark.parametrize("use_generic_base_class", [False, True])
 def test_lightning_cli_optimizers_and_lr_scheduler_with_link_to(use_generic_base_class):
     class MyLightningCLI(LightningCLI):
@@ -801,6 +802,7 @@ def __init__(self, optim1: dict, optim2: dict, scheduler: dict):
 
 
 @_xfail_python_ge_3_11_9
+@RunIf(min_torch="2.2")
 def test_lightning_cli_optimizers_and_lr_scheduler_with_callable_type():
     class TestModel(BoringModel):
         def __init__(