The Gunners have been heavily linked with the France international as they look to improve on a fifth-placed finish in the Premier League last season.
It seemed as if he was destined for Atletico Madrid, however, only for the Liga outfit's appeal against a transfer ban to be rejected.
Aulas has previously said he would not sell Lacazette unless a replacement was found, but now he is suggesting that there is no chance his prized asset will depart ahead of the 2017-18 season.
He is not ruling out a potential move to Atletico in January, however, with the player seemingly having his heart set on Diego Simeone's side.
When asked by Canal + if Lacazette would depart this summer, Aulas said: "I don't think so, no."
He did concede a move to Atletico was on the cards though, saying: "Yes, it's possible."