French international Lacazette, 24, has long been linked with a move to the Premier League having scored 48 goals over the last two Ligue 1 seasons.
“For a sale to be made, all three parties must agree. We have refused several offers, the most important from West Ham for 40 million euros and we refused it,” Aulas told French daily Le Progres.
“It is an answer that says I want to keep him, but I’m not sure because ultimately it is he who will decide.
“I do not want on August 28, ahead of the Champions League, to find ourselves in the same situation as Monaco (who sold Anthony Martial to Manchester United last summer).
“Ideally, he will stay. If he has an offer that he can’t refuse then it will come through me, and that’s it.”
Aulas also said that he is hoping to extend the contract of Lyon head coach Bruno Genesio, and bring in former Liverpool manager Gerard Houllier as general manager.