Sochaux, who hold the record of 66 seasons in the French first division, are bottom of the table with only two points from seven games.
"After the game, Eric offered to resign. But you don't take this kind of decision all of a sudden so we'll think about it in the next few hours and we'll hold a meeting tomorrow to decide what to do," Sochaux president Laurent Pernet told reporters.
Hely managed to save Sochaux from relegation after taking over in March last year.
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