The England international has fallen out of favour under Jose Mourinho this season, with the Chelsea boss preferring Cesar Azpilicueta at left-back.
The 33-year-old reportedly has a clause in his Chelsea contract that triggers a year's extension should he reach a certain number of games played this term.
But with Azpilicueta favoured, it looks unlikely at this of the season. And Cole, who has been linked with a number of clubs, could decide to end his eight-year association with Chelsea.
New York Red Bulls have both been mentioned as potential suitors for Cole, whose contract expires at Chelsea at the end of the season.
And he's not the only high profile Stamford Bridge star sweating over his Chelsea future. John Terry and Frank Lampard are both set for talks with the Blues hierarchy in the next few weeks.
The report claims Terry and Lampard expect to be offered one-year deals to stay at the club for at least the 2014-15 season.
But with Chelsea heavily linked with a summer move for Southampton star Luke Shaw, Cole could opt to move on at the end of the season.
The Saints left-back just received his first call-up to the England senior team, and the 18-year-old is thought to be a Chelsea target for the upcoming summer transfer window.
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