The 33-year-old is out of contract following eight years at Stamford Bridge.
The left-back, who retired from international football after being left out of England's World Cup squad, said on Twitter: "I am weighing up my options for playing next season with my agent and sadly it does not look like chelsea (sic) will be one of them.
"Thank u Chelsea FC for making my 8 years there a pleasure to work all the staff and players, we've been through a lot, good and bad.
"And of course the fans, how do I start, I can only say thank u for giving the boys confidence to win some amazing trophies, and once again.
"And this tweet is to the FANS that have stood buy (sic) me through thick and thin, I will always have u in my hearts, #cfcfans.
"And now I'll be looking for another journey in my life hope it can be like my others full of fun and of course WIN something."
Cole was kept out of the side by Cesar Azpilicueta for much of last season, making just 17 Barclays Premier League appearances, his lowest total in a single campaign for the club.
He was in tears after the final home game of the season, which now looks certain to have been his Stamford Bridge farewell.
The former Arsenal man was one of a trio of experienced players whose deals were up in the summer, along with Frank Lampard and John Terry, but captain Terry has since signed a one-year extension.
The future of Lampard, who will be 36 next month, is still undecided, with the midfielder's immediate focus on England and the World Cup.
Cole, who won 107 caps for England, will not be short of suitors with a number of top clubs already linked with the defender.
Since his move across London from Arsenal in 2006, he has won one league title, four FA Cups, the Europa League and, most memorably, the Champions League with the Blues.
Cole's contract expires on June 30.