diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index b23092e6f27e1..2363f3cda7da5 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -7450,6 +7450,18 @@ def ffill(
                         ChainedAssignmentError,
                         stacklevel=2,
                     )
+            elif not PYPY and not using_copy_on_write():
+                ctr = sys.getrefcount(self)
+                ref_count = REF_COUNT
+                if isinstance(self, ABCSeries) and hasattr(self, "_cacher"):
+                    # see https://github.com/pandas-dev/pandas/pull/56060#discussion_r1399245221
+                    ref_count += 1
+                if ctr <= ref_count:
+                    warnings.warn(
+                        _chained_assignment_warning_method_msg,
+                        FutureWarning,
+                        stacklevel=2,
+                    )
 
         return self._pad_or_backfill(
             "ffill",
@@ -7621,6 +7633,19 @@ def bfill(
                         ChainedAssignmentError,
                         stacklevel=2,
                     )
+            elif not PYPY and not using_copy_on_write():
+                ctr = sys.getrefcount(self)
+                ref_count = REF_COUNT
+                if isinstance(self, ABCSeries) and hasattr(self, "_cacher"):
+                    # see https://github.com/pandas-dev/pandas/pull/56060#discussion_r1399245221
+                    ref_count += 1
+                if ctr <= ref_count:
+                    warnings.warn(
+                        _chained_assignment_warning_method_msg,
+                        FutureWarning,
+                        stacklevel=2,
+                    )
+
         return self._pad_or_backfill(
             "bfill",
             axis=axis,
@@ -8215,6 +8240,18 @@ def interpolate(
                         ChainedAssignmentError,
                         stacklevel=2,
                     )
+            elif not PYPY and not using_copy_on_write():
+                ctr = sys.getrefcount(self)
+                ref_count = REF_COUNT
+                if isinstance(self, ABCSeries) and hasattr(self, "_cacher"):
+                    # see https://github.com/pandas-dev/pandas/pull/56060#discussion_r1399245221
+                    ref_count += 1
+                if ctr <= ref_count:
+                    warnings.warn(
+                        _chained_assignment_warning_method_msg,
+                        FutureWarning,
+                        stacklevel=2,
+                    )
 
         axis = self._get_axis_number(axis)
 
diff --git a/pandas/tests/copy_view/test_interp_fillna.py b/pandas/tests/copy_view/test_interp_fillna.py
index b2f3312abf8b5..8e2a62676da63 100644
--- a/pandas/tests/copy_view/test_interp_fillna.py
+++ b/pandas/tests/copy_view/test_interp_fillna.py
@@ -10,6 +10,7 @@
     Series,
     Timestamp,
     interval_range,
+    option_context,
 )
 import pandas._testing as tm
 from pandas.tests.copy_view.util import get_array
@@ -378,3 +379,14 @@ def test_interpolate_chained_assignment(using_copy_on_write, func):
         with tm.raises_chained_assignment_error():
             getattr(df[["a"]], func)(inplace=True)
         tm.assert_frame_equal(df, df_orig)
+    else:
+        with tm.assert_produces_warning(FutureWarning, match="inplace method"):
+            getattr(df["a"], func)(inplace=True)
+
+        with tm.assert_produces_warning(FutureWarning, match="inplace method"):
+            with option_context("mode.chained_assignment", None):
+                getattr(df[["a"]], func)(inplace=True)
+
+        with tm.assert_produces_warning(FutureWarning, match="inplace method"):
+            with option_context("mode.chained_assignment", None):
+                getattr(df[df["a"] > 1], func)(inplace=True)
diff --git a/pandas/tests/frame/methods/test_interpolate.py b/pandas/tests/frame/methods/test_interpolate.py
index 1ddab99947163..5f37ed6d9e18a 100644
--- a/pandas/tests/frame/methods/test_interpolate.py
+++ b/pandas/tests/frame/methods/test_interpolate.py
@@ -378,7 +378,8 @@ def test_interp_inplace(self, using_copy_on_write):
             assert return_value is None
             tm.assert_frame_equal(result, expected_cow)
         else:
-            return_value = result["a"].interpolate(inplace=True)
+            with tm.assert_produces_warning(FutureWarning, match="inplace method"):
+                return_value = result["a"].interpolate(inplace=True)
             assert return_value is None
             tm.assert_frame_equal(result, expected)