The 32-year-old made little impact during his time with the Scottish Premiership side.
The 32-year-old only signed an 18-month deal with the Hoops last October as Ronny Deila looked to provide star striker Leigh Griffiths with more support.
However, the former Chelsea and West Ham man failed to make any kind of impact for the Bhoys. His only goal came in the Scottish Cup tie with Stranraer in January, while his four Scottish Premiership appearances reaped no goals for the forward.
The Record's claim that a deal has now been agreed for the former England international to leave the club on a free transfer means that Cole has become the third forward to be axed since Brendan Rodgers arrived.
Both Anthony Stokes and Colin Kazim-Richards have been allowed to leave on free transfers, the Record reports. And despite Cole's departure leaving the Northern Irishman with few options up front, it is unlikely that many will be disappointed to see any of the trio move on.
Although Stokes' departure may have been met with slightly more mixed opinions - his loan spell at Hibernian hinted that he still had something to offer - Cole and Kazim-Richards offered Griffiths little support during their stints with the club, and their exits may free up space on the wage bill for Rodgers to pursue other targets.