Cole's loan agreement will reach a conclusion next summer, but he has refused to rule out the prospect of remaining in Ligue 1.
"I could join Lille permanently," he said.
"If they are happy with me, and vice versa, I don't see why not. Lille have quality players and there's an unbeatable mood in the dressing room. I benefit from it every day and I am enjoying myself.
"There is a superb team spirit at the club. I love playing here."