It was confirmed today that the North Londoners made an offer for the French international, which was immediately rebuffed
The 25 year-old French international is widely thought to be Andre Villas-Boas' top target for replacing Spurs' current first-choice stopper, and Premier League veteran, Brad Friedel.
However, Aulas has said that the north London club's bid to sign the played was swiftly rejected, and says they will only listen to financially attractive offers if Lloris himself asks for a move.
"Hugo wants to play in one of the best clubs in Europe," Aulas told French radio station RMC.
"This year there was an approach from Tottenham that was quickly rejected.
"If he absolutely wants to leave, we will look at the proposals but they must be consistent with what we want. If not, he will stay."
Goal.com exclusively revealed that Spurs would be turning their attention to Roma keeper Maarten Stekelenburg after their bids to sign Lloris faltered, who could be available for a cheaper price than his French counterpart.
The bad news comes on the same day that the agent of Uruguayan attacker Gaston Ramirez publically admitted that the 21-year-old had turned down an offer from the club.
However, up until now transfer business has been brusque and successful - with Spurs snatching Gylfi Sigurdsson from under the noses of Liverpool, and completing the signing of long-term target Jan Vertonghen.