I feel there is a strong need for this feature in media module. I am not sure if there is any way in media module we can do this.
I remember this was there earlier for filefield module something like file_path, but seems to be missing from media module. Have created a sandbox project for this purpose @ http://drupal.org/sandbox/piyuesh23/1525142.
Just need to be sure there is nothing of such sort before pushing it to a full project.