Report says, Atletico Madrid are also chasing Lacazette's signature, but Aulas confirmed that negotiations with the Spanish side broke down.
The Gunners remain in the hunt for Lacazette, but Aulas is keen to see the in-demand forward stay at Lyon, where he has a contract until 2019.
“Alexandre Lacazette was told he could leave. We had negotiations with Atletico," the president told Goal.com.
"Things did not work out. We now have a very nice offer from Arsenal. But for us he will not leave.”
"Today, the question of Alexandre leaving is annoying," he added. "For us, he won't leave. He'll be there for pre-season. Anyway, he's under contract."