Cole has done well at Lille and the player has indicated he would take a salary cut to stay in France.
“We have not started to do work for next season yet, neither for Cole nor for the other players”, Lille coach Rudi Garcia told La Voix du Nord.
“We are just concentrating on the last part of the season”, he added.
“He belongs to Liverpool, so it isn’t up to us to decide [if he will stay].”