The former Chelsea and England star is hoping to end his Anfield agony with a switch to the Ligue 1 champions after being denied a preferred move back to London with Tottenham
The 29-year-old midfielder travelled to France on Tuesday to hold talks with the Ligue 1 champions after it became clear he would not be granted his preferred move to Tottenham.
The former England international has also been strongly linked with a move to QPR but Cole is believed to have decided to join Lille due to the lure of Champions League football.
Cole is desperate to revive his career after making just eight Premier League starts last season following his high-profile free transfer from Chelsea.
Liverpool have been trying to offload Cole all summer to relieve the burden of his £90,000 weekly salary after buying midfielders Jordan Henderson, Charlie Adam and Stewart Downing.
Cole has found himself out of manager Kenny Dalglish's plans and has not even been named as a substitute in any of the club's four games so far this season.