diff --git a/src/transformers/cache_utils.py b/src/transformers/cache_utils.py
index 3c157018ecd214..f6791ead8bda43 100644
--- a/src/transformers/cache_utils.py
+++ b/src/transformers/cache_utils.py
@@ -1090,8 +1090,15 @@ def update(
             A tuple containing the updated key and value states.
         """
         cache_position = cache_kwargs.get("cache_position")
-        self.key_cache[layer_idx] = self.key_cache[layer_idx].to(device=key_states.device)
-        self.value_cache[layer_idx] = self.value_cache[layer_idx].to(device=value_states.device)
+        if key_states.device != self.key_cache[layer_idx].device:
+            # Note: The static cache is also used by `torch.export`. Attempting to call `.to()` on it
+            # will raise an error: "cannot mutate tensors with frozen storage" when using `torch.export`.
+            # Since `torch.export` currently works on "cpu", the workaround is to ensure that any device
+            # change is scoped within this conditional check to avoid tracing the device change code.
+            # See: https://github.com/pytorch/pytorch/issues/131679
+            self.key_cache[layer_idx] = self.key_cache[layer_idx].to(device=key_states.device)
+        if value_states.device != self.value_cache[layer_idx].device:
+            self.value_cache[layer_idx] = self.value_cache[layer_idx].to(device=value_states.device)
         k_out = self.key_cache[layer_idx]
         v_out = self.value_cache[layer_idx]