Spurs have been linked with the 25-year-old for some time and have reportedly had a bid for the France captain rejected by the Ligue 1 side who claim they have received no offers.
It was thought the chairman Daniel Levy had submitted a £12 million offer for Lloris and beat North London rivals Arsenal to the punch by capturing his signature.
But Aulas revealed the shot stopper won’t be leaving the Stade Gerland any time soon saying that the club would not welcome any approaches for his services.
“Tottenham made contact through [Lloris’] agent but there has been no concrete offer since,” he 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.”
New manager Andre Villas-Boas is determined to install a new number one between the sticks at White Hart Lane next summer with 41-year-old Brad Friedel coming towards the end of his career.
He said: “We will welcome any good addition to the squad.
“When I first signed here, there was no secret Tottenham would one day need a new long-term goalkeeper.
“I am 41, this could be my final season.
“I will do whatever asked of me, whether that is number one, two or three and will do it to the best of my ability.
“When you get older, it is easier to realise this is a team sport and the egos have to take a back seat if you want to be successful.”