But with Arsenal and the Red Bulls waiting in the wings, Cole should have plenty of offers should Chelsea fail to keep him.
Blues boss Jose Mourinho has dropped Cole this season, with Cesar Azpilicueta often operating at left back with Branislav Ivanovic on the right.
And he may decide to let the 33-year-old England defender go at the end of the season, with Chelsea's focus now on securing the world's best young players.
Liverpool boss Brendan Rodgers is a big fan of Cole having worked with him during his coaching stint at Stamford Bridge.
And the Anfield manager is looking for a new left-back with Aly Cissokho only a loan deal and likely to return to Valencia this summer.
A return to Arsenal would be a surprise considering the manner in which Cole left the Emirates Stadium the first time around.
And Mourinho has admitted that the Red Bulls could be a viable option for the Chelsea defender, with the lure of playing with Thierry Henry a potential sweetener.