According to the Daily Mail, Cole is adamant he will not sign the one-year extension on offer, and is preparing to speak with foreign clubs, including Real Madrid  and Paris Saint-Germain , in January.
The England international, who is back in Roy Hodgson's team for the World Cup qualifier against Poland on Tuesday, is a victim of Chelsea's new policy for players over the age of 30, the paper reported.
If Cole, 31, and Frank Lampard, who is also out of contract next summer, quit Stamford Bridge, it will be confirmation that Roman Abramovich is breaking up his Champions League-winning team, it said.
The paper further said Chelsea only offered Didier Drogba a one-year extension last summer, but he quit after failing to reach an agreement.
Cole, whose availability next summer has also alerted Manchester United manager Sir Alex Ferguson, has played in 188 out of a possible 235 games in the Premier League since signing from Arsenal six years ago, it added.
Cole missed the majority of those games in his first two seasons because of problems with his ankles, but he has been reliable in the past four years, the paper said. (ANI )