The 25-year-old has been linked with a move to White Hart Lane throughout the summer, but the French side have been adamant that they have no intention of selling the player.
However, Spurs have since made a formal approach for the Lyon stopper and Aulas says that only Lloris himself knows where his future lies.
"I'm not going to stick my neck out and say that [Lloris] will be here on September 4, even if I am hoping for that," Lloris told reporters.
“We have been in contact with Tottenham since yesterday (Sunday). Now, it's Hugo who holds the key."
Aulas went on to reveal Lyon had received offers from unnamed teams for striker Bafetimbi Gomis, but said Michel Bastos is yet to attract any fresh interest.
"For the moment, [Gomis] is at Lyon. We have more propositions coming from England for him. It's for us to discuss. Concerning Bastos, we have not had any new contact this weekend."
Aulas also stated he feels Paris Saint-Germain’s new-found wealth puts them in a position of responsibility to try and help improve the overall standard of French football.
"PSG have to find a method to help French clubs get bigger off their back, and they have to be generous," he explained.
"It would have been good if [Eden] Hazard had stayed in France, or if [Karim] Benzema, [Hatem] Ben Arfa and other France internationals had returned since the training fees would have strengthened French clubs."