The 33-year-old's contract at Stamford Bridge is set to expire at the end of June, while he retired from international duty after being left out of England's World Cup squad.
Jose Mourinho has preferred the right-footed Cesar Azpilicueta at left-back this season, but the 51-year-old was upbeat over Cole's future at the club and hinted a new deal could be reached.
However, late on Monday evening, Cole conceded an extension is unlikely and will now assess offers elsewhere ahead of the new season.
"I am weighing up my options for playing next season with my agent and sadly it does not look like Chelsea will be one of them," the left-back posted on Twitter.
Cole joined Chelsea from Arsenal in 2006 and went on to win the Premier League tile in 2010, the Champions League in 2012 and the FA Cup four times.