The 25-year-old confirmed he will leave the Ligue 1 club this week and said he had spoken to Atletico and would like to team up with Antoine Griezmann .
Although the France international said an answer would come "in a few months", Aulas has put an end to the speculation by admitting that an agreement is in place.
However, the move is far from certain, as Atletico are waiting on an appeal to the Court of Arbitration for Sport against their transfer ban.
Madrid were punished by FIFA for breaking regulations on signing youth players but are hoping to have it reduced to allow them to sign players this summer.
"Alex has a verbal agreement with a club, Atletico, but there is no certainty, since we have to wait for CAS to lift the ban," he told L'Equipe .
"We accepted Alex's request to discuss exclusively with this club, but the other side of that is that this transfer is made on our terms."
Lacazette scored twice as Lyon finished the season with a 3-3 draw against Nice on Saturday. He scored 28 goals in 30 Ligue 1 games.
The striker has been at the club since 2003, having risen through their youth system to become a star in the first team.
He is currently contracted to the club until 2019, but told L'Equipe it is "the right time" to move.
"I want to discover something else and to play at a different level. I know very well that on a European scale I am not yet well recognised.
"I want to see if I can answer the questions that people are asking, and to make further progress."