Lyon and United have reached an agreement in principle to bring Netherlands international Depay to France.
And Aulas expects the transfer to be wrapped up in two days as Lyon take a gamble on the 22-year-old, who has fallen out of favour under United manager Jose Mourinho
"We've bet on a player who wants to show his immense talent," Aulas told RMC Sport.
"There was a lot of interest in him from his time with Holland and in Eindhoven, where he had two fantastic seasons.
"When you see him developing, you get the impression that he really wants to show his immense talent. So we hope, as we hoped with the women's team by bringing in [US women's international] Alex Morgan, and we are not disappointed."
A big-money arrival from PSV in 2015-16, Depay has failed to live up to the hype at Old Trafford.
Since Louis van Gaal's departure in the off-season, Depay has only played 20 minutes of Premier League action.
Aulas added: "It was a dream because he corresponds exactly with the player we were looking for. In addition, he has a certain panache.
"It's true that Jose Mourinho didn't play him that much, so there was an opportunity for us to negotiate with Manchester United.
"For the moment, we've got an agreement in principle but we still need to write up a contract, which is a bit complicated because there are quite a few bonuses.
"This is a big operation, because I think it will be around 16.5million euros, with up to eight million in bonuses. It's a major investment.
"It's ongoing but it will take, I think, another 48 hours for him to be registered."