Les Dogues decided to part company with Frederic Antonetti last week following a disastrous start to the season, with a run of eight defeats in 10 matches leaving the club one off the bottom in Ligue 1.
Patrick Collot was placed in caretaker charge and did manage to pick up a point away at Nantes last weekend, but it is thought Lille want to have a permanent successor on board soon.
According to reports in France, Lille contacted Blanc to see if he would be interested in a return to management, with the World Cup-winning defender having been sacked by PSG at the end of last season.
Blanc is alleged to have turn down Lille’s offer to leave Vitor Pereira, the Fenerbahce head coach, and Marcelo Bielsa as the front runners for the post at the Stade Pierre-Mauroy.
Southampton have announced plans for a two-week tour of China as part of their pre-season preparations for the 2018-19 season.