Cole is out of contract this summer and is able to talk to foreign clubs over a pre contract agreement now.
The England left back has struggled to break into the Blues side this season under Jose Mourinho and despite still being first choice for Roy Hodgson and England, the 33 year old is set to leave Stamford Bridge this summer.
Chelsea are not prepared to offer big earner Cole a new deal, especially with his lack of first team input, and so one big final pay day looks certain.
Real Madrid have issues at left back with Ancelotti uncertain over both Fabio Coentrao and Marcelo, however they may look at a long term full back rather than Cole who will have two years maximum left of his peak.
The MLS is also an option for Cole, as well as a number of clubs in the Premier League willing to take a chance on him.