The former Arsenal defender recently retired from international duty after being omitted from England's World Cup squad and on Monday announced his intention to leave the Blues.
The former England left back, 33, will be one of the most coveted free transfers of the summer as he seeks “another journey in my life” following eight years at Stamford Bridge.
“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,” Cole wrote on Twitter on Monday night.
Liverpool boss Brendan Rodgers has made it clear he wants to add more stability to his defense next season and is believed to be weighing up a move for the experienced defender.
Rookie Jon Flanagan is on World Cup stand-by duty this summer after filling in so capably at left back in the second half of the season but his preferred position is at right back.
The Merseysiders had been in the market for another proven fullback in Bacary Sagna, 31, but the Arsenal man is on the brink of agreeing a free transfer to Manchester City.
Spurs are also monitoring Cole’s situation as they eye up contenders to fill the team’s problem left back slot next season.
Former manager Tim Sherwood had included Cole on a shortlist of key summer targets, although the identity of the new Tottenham manager could depend upon whether the Londoners make a concerted bid for the recently-retired England international.
There is also interest in Cole from MLS, although the player may want to ascertain the interest in the Premier League market before considering a move overseas.
Cole, who retired from international football having been left out of England’s World Cup squad, signaled the end of his Chelsea career with a series of tweets.
He wrote: “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 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.”
He also removed ‘Chelsea and England left-back’ from his Twitter biography.
Cole is a three-time Premier League champion, twice with Arsenal and once with Chelsea, and also has seven FA Cup winners' medals and won the 2008 League Cup.
He was part of Chelsea's Champions League winning team in 2012 and went on to win the Europa League a year later.