Lille are second from bottom in Ligue 1 after losing seven of their first 13 games in the league this season.
Lille were not immediately available for comment.
Bielsa, who coached Olympique de Marseille in Ligue 1 in 2014-15 before resigning after the first game of the following campaign, was named Lille coach during the close season.
The 62-year-old has previously managed the Argentina and Chile national teams and a host of clubs including Athletic Bilbao and Lazio.
(Reporting by Julien Pretot; Editing by Toby Davis)
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