diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index d89a1e012d5f8..96921fe0311c0 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -285,7 +285,7 @@ Datetimelike
 
 Timedelta
 ^^^^^^^^^
--
+- Bug in :func:`astype_nansafe` astype("timedelta64[ns]") fails when np.nan is included (:issue:`45798`)
 
 Time Zones
 ^^^^^^^^^^
diff --git a/pandas/core/dtypes/astype.py b/pandas/core/dtypes/astype.py
index 1e78bf0cd33ae..daae491b09c8a 100644
--- a/pandas/core/dtypes/astype.py
+++ b/pandas/core/dtypes/astype.py
@@ -27,6 +27,7 @@
     is_datetime64_dtype,
     is_datetime64tz_dtype,
     is_dtype_equal,
+    is_integer_dtype,
     is_object_dtype,
     is_timedelta64_dtype,
     pandas_dtype,
@@ -133,7 +134,7 @@ def astype_nansafe(
 
         raise TypeError(f"cannot astype a timedelta from [{arr.dtype}] to [{dtype}]")
 
-    elif np.issubdtype(arr.dtype, np.floating) and np.issubdtype(dtype, np.integer):
+    elif np.issubdtype(arr.dtype, np.floating) and is_integer_dtype(dtype):
         return _astype_float_to_int_nansafe(arr, dtype, copy)
 
     elif is_object_dtype(arr.dtype):
diff --git a/pandas/tests/series/methods/test_astype.py b/pandas/tests/series/methods/test_astype.py
index 630f4cc3194f4..6bdf93c43c986 100644
--- a/pandas/tests/series/methods/test_astype.py
+++ b/pandas/tests/series/methods/test_astype.py
@@ -600,3 +600,9 @@ def test_astype_from_categorical_with_keywords(self):
         exp = Series(Categorical(lst, categories=list("abcdef"), ordered=True))
         res = ser.astype(CategoricalDtype(list("abcdef"), ordered=True))
         tm.assert_series_equal(res, exp)
+
+    def test_astype_timedelta64_with_np_nan(self):
+        # GH45798
+        result = Series([Timedelta(1), np.nan], dtype="timedelta64[ns]")
+        expected = Series([Timedelta(1), NaT], dtype="timedelta64[ns]")
+        tm.assert_series_equal(result, expected)