The Spanish giants have been keeping and eye on Cole's situation and are reported to be willing to pay the £25million Chelsea would demand for his services.
The England left-back is facing a heavy fine and suspension following revelations of smuggling girls into his hotel room and trying to cover up an alleged extra marital affair while on a pre-season tour with the Blues.
Walk away: Cole could move to the Spanish top flight
Cole faces D-Day: Abramovich fury over alleged sex scandals could see full-back axedAnd as his marriage to pop star wife Cheryl looks over, a highly placed source told The Sun: 'Ashley is having a rough time at the moment. If he and Cheryl get divorced, why would he want to stay in this country?'
Madrid were linked with the 29-year-old defender when he left Arsenal for Chelsea in the summer of 2006 and will fancy their chances of landing the player if former Blues boss Jose Mourinho, as expected, takes over before the start of next season.
Chelsea advised Ashley Cole's mistress Ann Corbitt on how to stop infidelity claim No more sleaze or else! Roman gets tough with stars over sex scandalsRevealed: The Liverpool club secretary at the heart of Chelsea star Ashley Cole's sex scandal CHELSEA FC