diff --git a/pandas/core/internals/managers.py b/pandas/core/internals/managers.py
index e5f50bb35d6bd..9763d6664cd3b 100644
--- a/pandas/core/internals/managers.py
+++ b/pandas/core/internals/managers.py
@@ -1689,17 +1689,29 @@ def as_array(
         -------
         arr : ndarray
         """
+        passed_nan = lib.is_float(na_value) and isna(na_value)
+
         # TODO(CoW) handle case where resulting array is a view
         if len(self.blocks) == 0:
             arr = np.empty(self.shape, dtype=float)
             return arr.transpose()
 
-        # We want to copy when na_value is provided to avoid
-        # mutating the original object
-        copy = copy or na_value is not lib.no_default
-
         if self.is_single_block:
             blk = self.blocks[0]
+
+            if na_value is not lib.no_default:
+                # We want to copy when na_value is provided to avoid
+                # mutating the original object
+                if (
+                    isinstance(blk.dtype, np.dtype)
+                    and blk.dtype.kind == "f"
+                    and passed_nan
+                ):
+                    # We are already numpy-float and na_value=np.nan
+                    pass
+                else:
+                    copy = True
+
             if blk.is_extension:
                 # Avoid implicit conversion of extension blocks to object
 
@@ -1712,7 +1724,8 @@ def as_array(
             else:
                 arr = np.asarray(blk.get_values())
                 if dtype:
-                    arr = arr.astype(dtype, copy=False)
+                    arr = arr.astype(dtype, copy=copy)
+                    copy = False
 
             if copy:
                 arr = arr.copy()
@@ -1724,7 +1737,11 @@ def as_array(
             # The underlying data was copied within _interleave, so no need
             # to further copy if copy=True or setting na_value
 
-        if na_value is not lib.no_default:
+        if na_value is lib.no_default:
+            pass
+        elif arr.dtype.kind == "f" and passed_nan:
+            pass
+        else:
             arr[isna(arr)] = na_value
 
         return arr.transpose()
diff --git a/pandas/tests/frame/methods/test_to_numpy.py b/pandas/tests/frame/methods/test_to_numpy.py
index 532f7c87557c8..20e2a63cc793c 100644
--- a/pandas/tests/frame/methods/test_to_numpy.py
+++ b/pandas/tests/frame/methods/test_to_numpy.py
@@ -30,6 +30,10 @@ def test_to_numpy_copy(self):
         assert df.to_numpy(copy=False).base is arr
         assert df.to_numpy(copy=True).base is not arr
 
+        # we still don't want a copy when na_value=np.nan is passed,
+        #  and that can be respected because we are already numpy-float
+        assert df.to_numpy(copy=False, na_value=np.nan).base is arr
+
     def test_to_numpy_mixed_dtype_to_str(self):
         # https://github.com/pandas-dev/pandas/issues/35455
         df = DataFrame([[Timestamp("2020-01-01 00:00:00"), 100.0]])