Cole was in tears at the end of the Blues’ 0-0 draw with Norwich on Sunday and is expected to leave the club when his contract expires this summer.
The 33-year-old is resigned to leaving Chelsea, but he could stay in the Premier League with Liverpool showing interest.
Real Madrid are watching developments regarding Cole, while MLS outfit New York Red Bulls are also keen.
Chelsea boss Jose Mourinho wants to sign Seville’s Alberto Moreno, 21, as Cole’s replacement, having cooled his interest in Southampton star Luke Shaw.
That has in turn boosted Manchester United’s chances of securing the 18-year-old this summer.
Mourinho thinks Shaw is too expensive at £30million, amid reports United will pay that figure and hand the left-back a £100,000-a-week contract to bring him to Old Trafford.
But Chelsea are happy to sidestep Shaw and push ahead with a £15m move for Moreno.