diff --git a/sklearnex/cluster/k_means.py b/sklearnex/cluster/k_means.py
index f1567ad5c7..47ec5ca0d6 100644
--- a/sklearnex/cluster/k_means.py
+++ b/sklearnex/cluster/k_means.py
@@ -90,8 +90,11 @@ def _initialize_onedal_estimator(self):
 
             self._onedal_estimator = onedal_KMeans(**onedal_params)
 
-        def _onedal_fit_supported(self, method_name, X, y=None, sample_weight=None):
+        def _onedal_fit_supported(
+            self, method_name, _is_gpu, X, y=None, sample_weight=None
+        ):
             assert method_name == "fit"
+            assert _is_gpu is not None
 
             class_name = self.__class__.__name__
             patching_status = PatchingConditionsChain(f"sklearn.cluster.{class_name}.fit")
@@ -105,9 +108,12 @@ def _onedal_fit_supported(self, method_name, X, y=None, sample_weight=None):
                 )
             correct_count = self.n_clusters < sample_count
 
-            is_data_supported = (
-                _is_csr(X) and daal_check_version((2024, "P", 700))
-            ) or not issparse(X)
+            if not _is_gpu:
+                is_data_supported = (
+                    _is_csr(X) and daal_check_version((2024, "P", 700))
+                ) or not issparse(X)
+            else:
+                is_data_supported = not (_is_csr(X) or issparse(X))
 
             _acceptable_sample_weights = self._validate_sample_weight(sample_weight, X)
 
@@ -124,7 +130,7 @@ def _onedal_fit_supported(self, method_name, X, y=None, sample_weight=None):
                     ),
                     (
                         is_data_supported,
-                        "Supported data formats: Dense, CSR (oneDAL version >= 2024.7.0).",
+                        "Supported data formats: Dense, CSR (oneDAL version >= 2024.7.0 on CPU).",
                     ),
                 ]
             )
@@ -295,17 +301,25 @@ def _onedal_predict(self, X, sample_weight=None, queue=None):
 
             return self._onedal_estimator.predict(X, queue=queue)
 
-        def _onedal_supported(self, method_name, *data):
+        def _onedal_gpu_supported(self, method_name, *data):
+            _is_gpu = True
             if method_name == "fit":
-                return self._onedal_fit_supported(method_name, *data)
+                return self._onedal_fit_supported(method_name, _is_gpu, *data)
             if method_name in ["predict", "score"]:
                 return self._onedal_predict_supported(method_name, *data)
             raise RuntimeError(
                 f"Unknown method {method_name} in {self.__class__.__name__}"
             )
 
-        _onedal_gpu_supported = _onedal_supported
-        _onedal_cpu_supported = _onedal_supported
+        def _onedal_cpu_supported(self, method_name, *data):
+            _is_gpu = False
+            if method_name == "fit":
+                return self._onedal_fit_supported(method_name, _is_gpu, *data)
+            if method_name in ["predict", "score"]:
+                return self._onedal_predict_supported(method_name, *data)
+            raise RuntimeError(
+                f"Unknown method {method_name} in {self.__class__.__name__}"
+            )
 
         @wrap_output_data
         def fit_transform(self, X, y=None, sample_weight=None):