Lille want to keep on-loan Liverpool midfielder Joe Cole beyond his current season-long loan deal.
Cole, 30, joined the French Ligue 1 side in August and has become a regular for Rudi Garcia's team.
Club president Michel Seydoux said: "It is not a certainty that he will leave us at the end his contract.
"If he has a certain good feeling with Lille and we can make him an interesting offer, this is something we will look into," he added.
Cole, who will have two more years left on his Liverpool contract next summer, rejected interest from Aston Villa to join the current French champions on transfer deadline day in August.
He has regularly discussed how much he is enjoying France, having endured a frustrating year at Liverpool, who he joined on a free transfer from Chelsea in the summer of 2010.
He made just nine Premier League starts for the Anfield club last season and was allowed to leave after manager Kenny Dalglish signed Stewart Downing, Charlie Adam and Jordan Henderson during the summer.
But buoyed by his revival at Lille Cole, who won the last of his 56 England caps at the 2010 World Cup, has even set his sights on a recall to Fabio Capello's squad.
Lille won 2-0 at CSKA Moscow on Tuesday and must beat Trabzonspor, who lead them by a point, in their final group match to reach the Champions League knock-out phase.