Spurs have targeted the French goalkeeper as a long-term replacement for veteran Brad Friedel, but the president of the Ligue 1 side says they are determined not to sell
Several media sources had recently claimed that Spurs were close to agreeing a deal for the French international, while Arsenal had also been linked with a bid.
But Aulas says that no firm offer had been made by Andre Villas-Boas' side, and that unless Lloris is determined to leave, the club have no intention of selling him.
"Tottenham made contact through [Lloris'] agent but there has been no concrete offer since," Aulas explained. "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."
Reports claim that Tottenham had a £10 million bid for Lloris rejected recently, and were prepared to pay up to £12m to secure his signature as a long term replacement for 41-year-old Brad Friedel.
However, Lyon would not negotiate down from their £16 million asking price, and after playing in the French Super Cup against Montpellier on Saturday Lloris could be set to stay put.