"I'm not sure if a deal has been totally agreed. I know there have been talks," Liverpool boss Brendan Rodgers told reporters after Wednesday's 3-0 Premier League win over Sunderland when Cole did not make the squad.
Queens Park Rangers manager Harry Redknapp, who managed Cole at West Ham, said he had tried to sign the 31-year-old but that the player was heading for the Hammers.
Cole left Chelsea after a successful seven-year spell in 2010 but failed to make an impact at Anfield and spent last season at France's Lille. The last of his 56 England caps was also in 2010.
One of the most talked about English youngsters of his generation, Cole began his career at West Ham but angered fans of the East London club when moving across the capital to rivals Chelsea.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.