The prolific striker was bound for the Spanish capital at the start of the summer, only for Atleti to see their transfer ban upheld by the Court of Arbitration for Sport.
Lyon are refusing to sell Lacazette to the Gunners until a replacement is brought in, however, and they are also holding out for his £57m asking price to be met in full.
Providing another update on the ongoing saga, Aulas also revealed that his side are interested in Arsenal striker Olivier Giroud, who could possibly be used as a makeweight in any deal.
"I do not think that Alexandre Lacazette will leave this summer," he told Canal Plus. "I do not have anything to say about Olivier Giroud. We're interested. Things haven't advanced. But it's possible."
Lacazette has scored 129 goals in 275 appearances for Lyon, 37 of which came during the 2016-17 campaign.