The Gunners have been linked with a number of marquee striker additions this summer, and have now seemingly turned their attentions to the 26-year-old.
However, Aulas maintains that Lacazette will stay, after negotiations with Spanish club Atletico Madrid fell through.
"Today, the question of Alexandre leaving is annoying," he told reporters. For us, he won't leave. he'll be there for pre-season. Anyway, he's under contract.
"Alexandre knows our position. If he wants to try his hand somewhere else, there must be offers, which have gone straight to him. For the moment, I have no others. I don't know if he wants to leave. Maybe he'll give me a call.
"The ideal scenario would be that he stays and the goals we've set."
An initial report from Get France Football claimed that Aulas had spoken of an offer from Arsenal, though this has been proven as incorrect.
Aulas has previously invited an offer from PSG for Lacazette, having taken the stance that he would rather sell the striker to a domestic rival than sanction a move to England.
"I know Nasser suggested to Noel Le Graet [president of the French Football Federation] that he is not investing that much in French players because he thought other presidents of French clubs looked badly upon it," he told France Football earlier this week.
"I want him to know that if he makes an offer for Alexandre at least equal to that of the other clubs bidding for him, then Alex can go to Paris without problem.
"I am a businessman and a modern club president. Transfer money must be reinvested into French football, as I always did when we were at the peak of our powers.
"When transfer money is shared abroad, it strengthens our competitors instead."
Lacazette scored 37 goals in 45 appearances for Lyon in the 2016-17 season.