Joe Cole is set to remain at Lille beyond the end of his loan period, according to club president Michel Seydoux.
Cole, 30, has impressed since moving on-loan from Liverpool in the summer, making five appearances and forming an impressive partnership with Arsenal-target Eden Hazard.
Lille won 2-0 away at CSKA Moscow on Tuesday night to keep their hopes of qualifying for the Champions League knock-out phase alive.
"It is not a certainty that he will leave us at the end of 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 told RTL.
Cole, who still has two and half years left on his Liverpool contract, has revealed how much he is enjoying life in France, having experienced a frustrating spell on Merseyside after joining from Chelsea in the summer of 2010.
In an interview with the BBC, Cole admitted that joining Liverpool was a mistake.
"If I could go back and change things, I probably wouldn't have signed for Liverpool. I don't mean that in a nasty way though; it just didn't work. I came in at the wrong time; wrong style of manager; the team was low on confidence; the club was low.
"It was tough because I didn't play. I don't know ether it was a mistake for me, or for them - it just didn't fit last year. It could've worked, but it didn't.
However, Cole has no complaints about how he was treated at Anfield.
"The people there were good to me, as were the managers I played under; the people in and around the stadium; the fans; my teammates. I wish them well, and I'm still a Liverpool player".