diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index a5b4560a47bc4..258a0c3a5e99b 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -58,6 +58,7 @@ Other enhancements
 - :meth:`pandas.concat` will raise a ``ValueError`` when ``ignore_index=True`` and ``keys`` is not ``None`` (:issue:`59274`)
 - :meth:`str.get_dummies` now accepts a  ``dtype`` parameter to specify the dtype of the resulting DataFrame (:issue:`47872`)
 - Multiplying two :class:`DateOffset` objects will now raise a ``TypeError`` instead of a ``RecursionError`` (:issue:`59442`)
+- Arithmetic operations on :class:`Datetime` dataframe and series objects will result in :class:`Timedelta` values instead of ``TypeError`` (:issue: `59529`)
 - Restore support for reading Stata 104-format and enable reading 103-format dta files (:issue:`58554`)
 - Support passing a :class:`Iterable[Hashable]` input to :meth:`DataFrame.drop_duplicates` (:issue:`59237`)
 - Support reading Stata 102-format (Stata 1) dta files (:issue:`58978`)
diff --git a/pandas/core/internals/managers.py b/pandas/core/internals/managers.py
index aa4a785519051..bc3a9325f8abb 100644
--- a/pandas/core/internals/managers.py
+++ b/pandas/core/internals/managers.py
@@ -997,6 +997,8 @@ def _make_na_block(
             dtype = interleaved_dtype([blk.dtype for blk in self.blocks])
             if dtype is not None and np.issubdtype(dtype.type, np.floating):
                 fill_value = dtype.type(fill_value)
+            if dtype is not None and np.issubdtype(dtype.type, np.datetime64):
+                fill_value = np.datetime64("NaT")
 
         shape = (len(placement), self.shape[1])
 
diff --git a/pandas/tests/frame/test_arithmetic.py b/pandas/tests/frame/test_arithmetic.py
index e41a3b27e592c..5d861bdecd884 100644
--- a/pandas/tests/frame/test_arithmetic.py
+++ b/pandas/tests/frame/test_arithmetic.py
@@ -1038,9 +1038,9 @@ def test_frame_with_frame_reindex(self):
         [
             (1, "i8"),
             (1.0, "f8"),
-            (2**63, "f8"),
+            (2 ** 63, "f8"),
             (1j, "complex128"),
-            (2**63, "complex128"),
+            (2 ** 63, "complex128"),
             (True, "bool"),
             (np.timedelta64(20, "ns"), "<m8[ns]"),
             (np.datetime64(20, "ns"), "<M8[ns]"),
@@ -1147,6 +1147,33 @@ def test_arithmetic_midx_cols_different_dtypes_different_order(self):
         expected = DataFrame([[-1, 1], [-1, 1]], columns=midx)
         tm.assert_frame_equal(result, expected)
 
+    @pytest.mark.xfail(reason="NaT op NaT results in datetime instead of timedelta")
+    def test_arithmetic_datetime_df_series(self):
+        # GH#59529
+        df_datetime = DataFrame([[1, 2], [3, 4]]).astype("datetime64[ns]")
+        ser_datetime = Series([5, 6, 7]).astype("datetime64[ns]")
+        result = df_datetime - ser_datetime
+        expected = DataFrame(
+            [
+                [pd.Timedelta(-4), pd.Timedelta(-4), pd.Timedelta(pd.NaT)],
+                [pd.Timedelta(-2), pd.Timedelta(-2), pd.Timedelta(pd.NaT)],
+            ]
+        )
+        tm.assert_frame_equal(result, expected)
+
+    @pytest.mark.xfail(reason="NaT op NaT results in datetime instead of timedelta")
+    def test_arithmetic_timestamp_timedelta(self):
+        # GH#59529
+        df_timestamp = DataFrame([pd.Timestamp(1)])
+        ser_timedelta = Series([pd.Timedelta(2), pd.Timedelta(3)])
+        result = df_timestamp - ser_timedelta
+        expected = DataFrame(
+            [
+                [pd.Timestamp(-1), pd.NaT],
+            ]
+        )
+        tm.assert_frame_equal(result, expected)
+
 
 def test_frame_with_zero_len_series_corner_cases():
     # GH#28600
@@ -1913,7 +1940,7 @@ def test_pow_with_realignment():
     left = DataFrame({"A": [0, 1, 2]})
     right = DataFrame(index=[0, 1, 2])
 
-    result = left**right
+    result = left ** right
     expected = DataFrame({"A": [np.nan, 1.0, np.nan]})
     tm.assert_frame_equal(result, expected)