Rafael Benitez has been a long-term admirer of the France international and reportedly looked to sign him in the pre-season transfer window before returning for him now.
But Aulas is determined to keep the 24-year-old in Ligue 1 for now and claimed he has convinced Gonalons that he should remain at the Stade de Gerland for the foreseeable future.
"On his departure, I answered no," Aulas told the club's official website.
"I have talked with the president of Napoli (Aurelio De Laurentiis) to warn him. Max will remain at Lyon.
"The decision was taken Monday night. This decision was taken in consultation with Remi Garde.
"The proposal amounted to €17million on Monday night, but I have convinced Max that his future remains at Lyon at least until the end of season.
"Max must go to a big club, should there be an undeniable interest.
"OL, it has a very important status and as he hopes to go to Brazil (with France for the 2014 FIFA World Cup).
"Could he start in Naples after the end of the season? There's no decision taken.
"Maxime is a boy of quality. At the end of it, he was flattered that a big club is interested in him."
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