The 29-year-old has impressed for the French side since joining the club on a season-long loan move from Liverpool over the summer.
Cole said: “I could join Lille permanently. 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.”
