"Alexandre is irreplaceable," Aulas told Foot Mercato. "It would be malpractice to sell him."
While it is unclear whether Aulas was speaking before or after news of Arsenal's formal approach became public, he appears determined to hold on to the France international.
"I find him to be completely calm," Aulas said of Lacazette. "I think he's going to have a very good Champions League and I honestly see Alexandre getting 27 to 30 goals again in the French league.
"For me, he'll be ahead of [PSG forward Edinson] Cavani this year for the number of goals scored. And I see him putting in an incredible performance in the Champions League as well.
"For all these reasons, I can't imagine that he might be able to leave and I think that he too wants to have a complete season with OL. Alexandre will be Lyonnais."