Juninho, 42, represented Lyon as a player between 2001 and 2009, scoring 75 times in 248 league appearances for the French giants, who won seven Ligue 1 titles during the Brazilian's time at the club.
The 40-time Brazil international later turned out for Vasco da Gama and New York Red Bulls, but Aulas is "hopeful of bringing Juninho back" as Lyon's new sporting director.
"We are not far from succeeding. At least I hope so. I'm hopeful of bringing Juninho back. We have been talking to him for a month," Aulas told reporters. "We are doing everything to convince him. He is a talented, thoughtful boy.
"He asks a lot of questions. We are working to define the elements that should enable him to give us an agreement in the coming days. He left part of his heart in Lyon, where the public adored him. It would be a win-win for him and the club.
"I think he really wants [to return], his wife also. If he returns, it is to win and carry Lyon to the highest level. It would be a new pressure. He has to make an internal and family choice to go 'into business' and live with the pressure related to coaches or leaders."