Cole has struggled for first team football since being dropped by Jose Mourinho following the Blues’ 2-0 defeat to Newcastle last month.
Mourinho has moved Spaniard Cesar Azpilicueta to left back, and his impressive performances have seen Cole drop down the pecking order.
Cole – who turns 33 this month – is desperate for game time in order to prove to England boss Roy Hodgson, that he should be first choice left back for next summer’s World Cup in Brazil.
Everton full back Leighton Baines is also battling for the first choice spot, so Cole is aware he may need as early as January in order to get the first team football he needs.
Some reports suggest Cole could be reunited with former Arsenal teammate Thierry Henry at the New York Red Bulls, while other reports claim David Beckham’s former club LA Galaxy also want the England defender.
Cole’s current one-year deal – worth a reported £60,000 a week – is set to expire in the summer, meaning Chelsea may want to sell him in a cut price deal in January.
The Blues are set to enter the transfer market to find a long term replacement, with second choice Ryan Bertrand currently being monitored by Liverpool.