Speculation linking Herve Renard with the Lille job took on new significance after he left his role with Ivory Coast on Friday.
Herve Renard has left his position as Ivory Coast coach as speculation mounts that he will succeed Rene Girard at Lille.
Renard guided Ivory Coast to the Africa Cup of Nations title this year and had 18 months remaining on his deal.
It was announced this week that Girard will leave Lille at the end of the Ligue 1 season, but Renard gave no hint over his future as he offered an emotional farewell to Ivory Coast.
"At the time when I decided to leave...I wanted to thank from the bottom of the heart all the people who have [played a role in] the victory of the Africa Cup of Nations last February," the 46-year-old said in a statement.
"Thank you to the fervour of an entire people who waited for 23 years [for] a coronation in the most beautiful competitions of the continent Africa.
"The images of our return home, a few hours after our success against Ghana, will remain engraved forever in my head."