The Reds are reported to have offered the England international a lucrative deal to tempt him up north, and away from the North London clubs that can offer him Champions League football this season.
Cole’s contract at Stamford Bridge expired at the end of June, and is now considering his options.
Liverpool boss Roy Hodgson refused to rule out speculation linking the club with the 28-year-old. He said, “As far as I know, Joe Cole is still a player looking for a club.
“I know we’ve been connected with him, and it’s good to know we’re connected with players of that quality, but I don’t have anything to report on the subject.
“I haven’t had any discussions with him, but I had a brief chat a while back.”