Platt, 42, is believed to have been approached by current caretaker manager and technical director Dario Gradi over a potential return to Gresty Road.
The struggling Railwaymen are on the lookout for a new boss following their decision to part company with first-team coach Steve Holland last month.
Crewe are currently rock-bottom of the League One table but Platt, who has been out of management since leaving his role as England Under-21 coach in 2004, has turned down the approach.
The ex-Nottingham Forest boss made over 100 appearances for the Alex before leaving to join Aston Villa in 1988.