France Football says Lille are eyeing the midfielder and contact has been made with his camp.
While no approach has been made to Chelsea, LOSC have made it clear to Boga they're eager to sign him.
Last month, Boga said: "I have clear ideas for my future. This is my third season of loan. I gained a lot of experience this season and I feel ready for next year either to fight to try to impose myself at Chelsea or to leave the club. I do not really want another loan."