diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index 7a2175a364a8a..a46e74ae15a06 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -1733,6 +1733,8 @@ def maybe_cast_to_datetime(
                     except ValueError:
                         # TODO(GH#40048): only catch dateutil's ParserError
                         #  once we can reliably import it in all supported versions
+                        if is_timedelta64:
+                            raise
                         pass
 
         # coerce datetimelike to object
diff --git a/pandas/tests/frame/test_constructors.py b/pandas/tests/frame/test_constructors.py
index b76a44b3c86be..5edeb72725d2f 100644
--- a/pandas/tests/frame/test_constructors.py
+++ b/pandas/tests/frame/test_constructors.py
@@ -89,7 +89,12 @@ def test_array_of_dt64_nat_with_td64dtype_raises(self, frame_or_series):
         if frame_or_series is DataFrame:
             arr = arr.reshape(1, 1)
 
-        msg = "Could not convert object to NumPy timedelta"
+        msg = "|".join(
+            [
+                "Could not convert object to NumPy timedelta",
+                "Invalid type for timedelta scalar: <class 'numpy.datetime64'>",
+            ]
+        )
         with pytest.raises(ValueError, match=msg):
             frame_or_series(arr, dtype="m8[ns]")
 
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index ab484e7ae9d8a..75474a29169a7 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -1351,7 +1351,12 @@ def test_constructor_dtype_timedelta64(self):
             td.astype("int32")
 
         # this is an invalid casting
-        msg = "Could not convert object to NumPy timedelta"
+        msg = "|".join(
+            [
+                "Could not convert object to NumPy timedelta",
+                "Could not convert 'foo' to NumPy timedelta",
+            ]
+        )
         with pytest.raises(ValueError, match=msg):
             Series([timedelta(days=1), "foo"], dtype="m8[ns]")