Spurs have been linked with the France captain but the club claim no offer has been made and the Ligue 1 side say they would not welcome one.
"Tottenham made contact through [Lloris'] agent but there has been no concrete offer since," Aulas said. "I don't think they really want him, but we really want to keep him.
"He will stay at Lyon unless he absolutely wants to go. The best present we can give to the fans is finding a way to keep him. We will try to do just that."
Arsenal have also been linked with a move for the 25-year-old, who has three years left on his current contract after signing a two-year extension last October.
Lloris started for Lyon in their Trophee des Champions triumph over Montpellier in New York on Saturday.