The on-loan attacker is said to be keen to remain with the Ligue 1 outfit, though Michel Seydoux has conceded the French side may not be able to match his salary
Cole is currently on a season-long loan with the Ligue 1 club, having failed to impress on Merseyside after being signed by former Reds boss Roy Hodgson.
The England international is now said to be keen to stay with Lille, though Seydoux admits the club may not be in the financial position to keep Cole.
|16/1||Lille are 16/1 to win Ligue 1 this season with William Hill|
"Joe Cole has spoken and I thought it was great. It's rare that an English player comes to France and says he wants to continue," he told RMC.
“A discussion was held today. I do not make money. You must be reasonable. We'll see when we will do the main choices.”
Lille are the in-form team in Ligue 1 at the moment, notching five wins from their last six games as they push for Champions League football next year.
The club currently sit third in the league, five points off big-spenders Paris Saint-Germain and a place in Europe’s premier club competition.
The two clubs come face-to-face this weekend in a potentially pivotal clash and Seydoux admits the team’s position in the league may have an effect on the outcome of Cole’s future.
He continued: “The final ranking will be important in the transfer window."