diff --git a/Doc/library/shutil.rst b/Doc/library/shutil.rst
index 3a4631e7c657fe..1968f0dcf75a51 100644
--- a/Doc/library/shutil.rst
+++ b/Doc/library/shutil.rst
@@ -122,12 +122,15 @@ Directory and files operations
    .. versionchanged:: 3.3
       Added *follow_symlinks* argument.
 
-.. function:: copystat(src, dst, *, follow_symlinks=True)
+.. function:: copystat(src, dst, *, follow_symlinks=True, preserve_timestamps=True)
 
-   Copy the permission bits, last access time, last modification time, and
-   flags from *src* to *dst*.  On Linux, :func:`copystat` also copies the
-   "extended attributes" where possible.  The file contents, owner, and
-   group are unaffected.  *src* and *dst* are :term:`path-like objects <path-like object>` or path
+   Copy the permission bits and flags from *src* to *dst*; the last access
+   time and last modification time are also copied if *preserve_timestamps*
+   is true (on Windows platforms, *preserve_timestamps* is ignored).
+   On Linux, :func:`copystat` also copies the "extended attributes"
+   where possible. The file contents, owner, and group are unaffected.
+
+   *src* and *dst* are :term:`path-like objects <path-like object>` or path
    names given as strings.
 
    If *follow_symlinks* is false, and *src* and *dst* both
@@ -169,6 +172,9 @@ Directory and files operations
    .. versionchanged:: 3.3
       Added *follow_symlinks* argument and support for Linux extended attributes.
 
+   .. versionchanged:: next
+      Added the *preserve_timestamps* argument.
+
 .. function:: copy(src, dst, *, follow_symlinks=True)
 
    Copies the file *src* to the file or directory *dst*.  *src* and *dst*
@@ -201,7 +207,7 @@ Directory and files operations
       copy the file more efficiently. See
       :ref:`shutil-platform-dependent-efficient-copy-operations` section.
 
-.. function:: copy2(src, dst, *, follow_symlinks=True)
+.. function:: copy2(src, dst, *, follow_symlinks=True, preserve_timestamps=True)
 
    Identical to :func:`~shutil.copy` except that :func:`copy2`
    also attempts to preserve file metadata.
@@ -215,6 +221,9 @@ Directory and files operations
    it can; :func:`copy2` never raises an exception because it
    cannot preserve file metadata.
 
+   On non-Windows platforms, if *preserve_timestamps* is false,
+   the last access time and last modification time are not copied.
+
    :func:`copy2` uses :func:`copystat` to copy the file metadata.
    Please see :func:`copystat` for more information
    about platform support for modifying symbolic link metadata.
@@ -233,6 +242,9 @@ Directory and files operations
       copy the file more efficiently. See
       :ref:`shutil-platform-dependent-efficient-copy-operations` section.
 
+   .. versionadded:: next
+      Added the *preserve_timestamps* argument.
+
 .. function:: ignore_patterns(*patterns)
 
    This factory function creates a function that can be used as a callable for
diff --git a/Lib/shutil.py b/Lib/shutil.py
index 8d8fe145567822..266b64fcebbbb6 100644
--- a/Lib/shutil.py
+++ b/Lib/shutil.py
@@ -406,14 +406,15 @@ def _copyxattr(src, dst, *, follow_symlinks=True):
     def _copyxattr(*args, **kwargs):
         pass
 
-def copystat(src, dst, *, follow_symlinks=True):
+def copystat(src, dst, *, follow_symlinks=True, preserve_timestamps=True):
     """Copy file metadata
 
-    Copy the permission bits, last access time, last modification time, and
-    flags from `src` to `dst`. On Linux, copystat() also copies the "extended
-    attributes" where possible. The file contents, owner, and group are
-    unaffected. `src` and `dst` are path-like objects or path names given as
-    strings.
+    Copy the permission bits and flags from `src` to `dst`; the last access
+    time and last modification time are also copied if `preserve_timestamps`
+    is true. On Linux, copystat() also copies the "extended attributes" where
+    possible. The file contents, owner, and group are unaffected.
+
+    `src` and `dst` are path-like objects or path names given as strings.
 
     If the optional flag `follow_symlinks` is not set, symlinks aren't
     followed if and only if both `src` and `dst` are symlinks.
@@ -443,8 +444,9 @@ def lookup(name):
     else:
         st = lookup("stat")(src, follow_symlinks=follow)
     mode = stat.S_IMODE(st.st_mode)
-    lookup("utime")(dst, ns=(st.st_atime_ns, st.st_mtime_ns),
-        follow_symlinks=follow)
+    if preserve_timestamps:
+        lookup("utime")(dst, ns=(st.st_atime_ns, st.st_mtime_ns),
+            follow_symlinks=follow)
     # We must copy extended attributes before the file is (potentially)
     # chmod()'ed read-only, otherwise setxattr() will error with -EACCES.
     _copyxattr(src, dst, follow_symlinks=follow)
@@ -490,7 +492,7 @@ def copy(src, dst, *, follow_symlinks=True):
     copymode(src, dst, follow_symlinks=follow_symlinks)
     return dst
 
-def copy2(src, dst, *, follow_symlinks=True):
+def copy2(src, dst, *, follow_symlinks=True, preserve_timestamps=True):
     """Copy data and metadata. Return the file's destination.
 
     Metadata is copied with copystat(). Please see the copystat function
@@ -527,7 +529,8 @@ def copy2(src, dst, *, follow_symlinks=True):
                 raise
 
     copyfile(src, dst, follow_symlinks=follow_symlinks)
-    copystat(src, dst, follow_symlinks=follow_symlinks)
+    copystat(src, dst, follow_symlinks=follow_symlinks,
+             preserve_timestamps=preserve_timestamps)
     return dst
 
 def ignore_patterns(*patterns):