diff --git a/pandas/tests/copy_view/test_interp_fillna.py b/pandas/tests/copy_view/test_interp_fillna.py
index e15509c5140dd..d0c4fa53faab9 100644
--- a/pandas/tests/copy_view/test_interp_fillna.py
+++ b/pandas/tests/copy_view/test_interp_fillna.py
@@ -165,7 +165,7 @@ def test_interpolate_object_convert_no_op(using_copy_on_write, using_infer_strin
         df.interpolate(method="pad", inplace=True)
 
     # Now CoW makes a copy, it should not!
-    if using_copy_on_write:
+    if using_copy_on_write and not using_infer_string:
         assert df._mgr._has_no_reference(0)
         assert np.shares_memory(arr_a, get_array(df, "a"))
 
diff --git a/pandas/tests/copy_view/test_replace.py b/pandas/tests/copy_view/test_replace.py
index 9e24ce319e3bf..c260ad9604616 100644
--- a/pandas/tests/copy_view/test_replace.py
+++ b/pandas/tests/copy_view/test_replace.py
@@ -357,11 +357,14 @@ def test_replace_empty_list(using_copy_on_write):
 
 
 @pytest.mark.parametrize("value", ["d", None])
-def test_replace_object_list_inplace(using_copy_on_write, value):
+def test_replace_object_list_inplace(using_copy_on_write, using_infer_string, value):
     df = DataFrame({"a": ["a", "b", "c"]}, dtype=object)
     arr = get_array(df, "a")
-    df.replace(["c"], value, inplace=True)
-    if using_copy_on_write or value is None:
+    # with future.infer_string we get warning about object dtype getting cast
+    warning = FutureWarning if using_infer_string and value is not None else None
+    with tm.assert_produces_warning(warning):
+        df.replace(["c"], value, inplace=True)
+    if (using_copy_on_write or value is None) and not warning:
         assert np.shares_memory(arr, get_array(df, "a"))
     else:
         # This could be inplace