Marcelo Bielsa has met representatives of Gerard Lopez, the man expected to take over Lille, several times in recent weeks to discuss becoming their coach, Canal+ has claimed.
Bielsa, 61, has been without a club since leaving Lazio just two days after his appointment as coach last summer.
The former Argentina and Chile coach enjoys an excellent reputation in France for his work at Marseille during the 2014-15 season when his side played some of the best football in Ligue 1.
Lille are without a permanent first-team coach since Frederic Antonetti was relieved of his duties last week.
His assistant, Patrick Collot, has picked up four points from the two games he has been in interim charge, including Tuesday's 4-2 defeat of Caen that lifted the club out of the relegation zone.
Lille are set to be bought by Lopez, a former president of Formula One team Lotus, who is seeking a high-profile coach to lead his project, and Canal+ reported on Wednesday that Bielsa is his No. 1 target.
The ex-Athletic Bilbao coach has reportedly already met Luis Campos, who earlier this season left Monaco to join Lopez's project, which is expected to complete a buy-out of current Lille owner Michel Seydoux in the coming weeks.
Lopez, 44, was previously in talks to purchase Marseille before American Frank McCourt completed a €45 million deal in October.
The Luxembourg businessman told RMC in August that he had already met Bielsa in an attempt to get him to return to the Stade Velodrome, which he left after the opening game of the 2015-16 campaign citing differences with the club's board.
"The only bit of truth in what I have read is that I have spoken a lot to Marcelo Bielsa to get him to come back," Lopez said when asked about the flurry of speculation and rumour around his potential OM buy-out. "I've spoken to him every week since the start of the project."