The Liverpool striker, who moved to France on loan last summer, has expressed a desire to remain in France.
Club president Michel Seydoux has admitted, however, that he may not able to afford the England international's £90,000-a-week wages.
"It's rare that an England international comes to France and that he then publicly declares he wants to stay. We will see. I haven't found a machine yet that lets you make beautiful bank notes by pedalling. It's true that the league table will have a bearing on Lille's recruitment," he told reporters.
Lille currently occupy third spot in Ligue 1.