Gunners boss Arsene Wenger confirmed his interest in the 22-year-old in May, but Aulas is confident the France international will stay with les Gones.
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The club are set to hold a meeting with Grenier to discuss his future on Monday, and the young playmaker is less sure of his future at the Ligue 1 club than Aulas.
“Today, I honestly cannot answer that, my future is not fixed,” said Grenier when asked if he will remain at Lyon.
“I have an appointment with the president, the coach and my representatives in order to discuss all this. A meeting that can come very quickly, surely right after out return from training camp [in Tignes].”
Aulas also discussed the future of striker Bafetimbi Gomis, a target for a number of Premier League clubs, but revealed that the 27-year-old forward was not keen on any of the proposed moves.
“Bafe [Gomis] is studying a certain number of offers like we told him to,” added Aulas.
“We showed him three proposals, they do not seem to suit him. We will try to find others that suit him better.”