The 25-year-old has been strongly linked with a move to White Hart Lane this summer, with Spurs having already shown their interest in the France international.
"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," said Aulas.
"We have been in contact with Tottenham since yesterday (Sunday). Now it's Hugo who holds the key."
Lloris joined Lyon from Nice in 2008.