diff --git a/CHANGELOG.md b/CHANGELOG.md
index 81846809fbf85..bf47285ba7923 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -170,6 +170,9 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 ### Fixed
 
+- Sanitize `None` params during pruning ([#6836](https://github.com/PyTorchLightning/pytorch-lightning/pull/6836))
+
+
 - Made the `Plugin.reduce` method more consistent across all Plugins to reflect a mean-reduction by default ([#6011](https://github.com/PyTorchLightning/pytorch-lightning/pull/6011))
 
 
diff --git a/pytorch_lightning/callbacks/pruning.py b/pytorch_lightning/callbacks/pruning.py
index 3f82ab3565403..36622af0edaff 100644
--- a/pytorch_lightning/callbacks/pruning.py
+++ b/pytorch_lightning/callbacks/pruning.py
@@ -422,7 +422,9 @@ def sanitize_parameters_to_prune(
         current_modules = [m for m in pl_module.modules() if not isinstance(m, _MODULE_CONTAINERS)]
 
         if parameters_to_prune is None:
-            parameters_to_prune = [(m, p) for p in parameters for m in current_modules if hasattr(m, p)]
+            parameters_to_prune = [
+                (m, p) for p in parameters for m in current_modules if getattr(m, p, None) is not None
+            ]
         elif (
             isinstance(parameters_to_prune, (list, tuple)) and len(parameters_to_prune) > 0
             and all(len(p) == 2 for p in parameters_to_prune)
diff --git a/tests/callbacks/test_pruning.py b/tests/callbacks/test_pruning.py
index e42689a25d8aa..1e39cc9c330b0 100644
--- a/tests/callbacks/test_pruning.py
+++ b/tests/callbacks/test_pruning.py
@@ -36,7 +36,7 @@ def __init__(self):
         self.layer = Sequential(
             OrderedDict([
                 ("mlp_1", nn.Linear(32, 32)),
-                ("mlp_2", nn.Linear(32, 32)),
+                ("mlp_2", nn.Linear(32, 32, bias=False)),
                 ("mlp_3", nn.Linear(32, 2)),
             ])
         )
@@ -85,7 +85,10 @@ def train_with_pruning_callback(
     if parameters_to_prune:
         pruning_kwargs["parameters_to_prune"] = [(model.layer.mlp_1, "weight"), (model.layer.mlp_2, "weight")]
     else:
-        pruning_kwargs["parameter_names"] = ["weight"]
+        if isinstance(pruning_fn, str) and pruning_fn.endswith("_structured"):
+            pruning_kwargs["parameter_names"] = ["weight"]
+        else:
+            pruning_kwargs["parameter_names"] = ["weight", "bias"]
     if isinstance(pruning_fn, str) and pruning_fn.endswith("_structured"):
         pruning_kwargs["pruning_dim"] = 0
     if pruning_fn == "ln_structured":
@@ -249,14 +252,14 @@ def test_multiple_pruning_callbacks(tmpdir, caplog, make_pruning_permanent: bool
     actual = [m for m in actual if m.startswith("Applied")]
     assert actual == [
         "Applied `L1Unstructured`. Pruned: 0/1122 (0.00%) -> 544/1122 (48.48%)",
-        "Applied `L1Unstructured` to `Linear(in_features=32, out_features=32, bias=True).weight` with amount=0.5. Pruned: 0 (0.00%) -> 506 (49.41%)",  # noqa: E501
-        "Applied `L1Unstructured` to `Linear(in_features=32, out_features=2, bias=True).weight` with amount=0.5. Pruned: 0 (0.00%) -> 38 (59.38%)",  # noqa: E501
+        "Applied `L1Unstructured` to `Linear(in_features=32, out_features=32, bias=True).weight` with amount=0.5. Pruned: 0 (0.00%) -> 500 (48.83%)",  # noqa: E501
+        "Applied `L1Unstructured` to `Linear(in_features=32, out_features=2, bias=True).weight` with amount=0.5. Pruned: 0 (0.00%) -> 44 (68.75%)",  # noqa: E501
         "Applied `RandomUnstructured`. Pruned: 544/1122 (48.48%) -> 680/1122 (60.61%)",
-        "Applied `RandomUnstructured` to `Linear(in_features=32, out_features=32, bias=True).weight` with amount=0.25. Pruned: 506 (49.41%) -> 633 (61.82%)",  # noqa: E501
-        "Applied `RandomUnstructured` to `Linear(in_features=32, out_features=2, bias=True).weight` with amount=0.25. Pruned: 38 (59.38%) -> 47 (73.44%)",  # noqa: E501
+        "Applied `RandomUnstructured` to `Linear(in_features=32, out_features=32, bias=True).weight` with amount=0.25. Pruned: 500 (48.83%) -> 635 (62.01%)",  # noqa: E501
+        "Applied `RandomUnstructured` to `Linear(in_features=32, out_features=2, bias=True).weight` with amount=0.25. Pruned: 44 (68.75%) -> 45 (70.31%)",  # noqa: E501
         "Applied `L1Unstructured`. Pruned: 680/1122 (60.61%) -> 884/1122 (78.79%)",
-        "Applied `L1Unstructured` to `Linear(in_features=32, out_features=32, bias=True).weight` with amount=0.5. Pruned: 633 (61.82%) -> 828 (80.86%)",  # noqa: E501
-        "Applied `L1Unstructured` to `Linear(in_features=32, out_features=2, bias=True).weight` with amount=0.5. Pruned: 47 (73.44%) -> 56 (87.50%)",  # noqa: E501
+        "Applied `L1Unstructured` to `Linear(in_features=32, out_features=32, bias=True).weight` with amount=0.5. Pruned: 635 (62.01%) -> 830 (81.05%)",  # noqa: E501
+        "Applied `L1Unstructured` to `Linear(in_features=32, out_features=2, bias=True).weight` with amount=0.5. Pruned: 45 (70.31%) -> 54 (84.38%)",  # noqa: E501
     ]
 
     filepath = str(tmpdir / "foo.ckpt")