Lille won their first league game under Bielsa before picking up just two points from the next six matches, with pressure building on the former Argentina coach after Friday's 4-0 defeat at home to Monaco.
The 2010-11 champions are now 18th in the table, but owner Gerard Lopez is sticking by Bielsa, believing he can inspire change.
"I am well aware of our position, but I am also aware that it is only after matchday seven," Lopez told Telefoot. "It is up to Marcelo Bielsa to find the way.
"I do not ask myself [about Bielsa's future] — I think about the next game. We cannot manage a club, a team, having these kind of thoughts."
Bielsa, who signed a two-year contract in May, takes Lille to 16th-placed Amiens on Saturday.