Cole could join any other club in January if the Blues don't offer him an improved deal, which he thinks he deserves after diligently serving for around six years.
"Mr. Abramovich has a rule that anyone over 30 can only be given a one-year extension, but it's madness in Ashley's case," the Sun quoted a club insider, as saying.
"Everyone knows he's the best left-back in the world. He trains hard, really looks after himself and can play at this level for many more years to come. There isn't a club in the world who wouldn't want Ashley on a free," he added.
Real Madrid boss Jose Mourinho is a huge admirer of his former player and if Cole does quit, Paris St Germain and Zenit St Petersburg would offer mega-money deals.
Cole was willing to see out his career at Stamford Bridge, so this latest development has stunned insiders.
And last night, there was further evidence that Chelsea is ready to lose Cole when his understudy Ryan Bertrand signed a new five-year contract. (ANI )