The 2011 French champions could not be reached for official confirmation.
The 33-year-old Landreau asked to leave the club having been at odds with coach Rudi Garcia and other staff members for months, according to media reports.
The keeper, who has played 568 French league games for Nantes, Paris St Germain and Lille, was a key player when the Northerners clinched their first title in more than 50 years in 2011.
Landreau made his debut for Nantes at the of 17. He has 11 caps for France and has been called up as a reserve keeper for all the games since Didier Deschamps took charge of the national team in July.
Lille, 10th in the Ligue 1 standings and 10 points behind leaders Lyon, signed Stade Brest keeper Steeve Elana in the off-season to force competition in the position.
They visit second-bottom Sochaux on Saturday.
(Writing by Gregory Blachier; Editing by Ed Osmond)