The France captain has been made available for transfer if a club can make an acceptable offer before July 15, giving potential suitors a slim window of opportunity.
Though Arsenal were initially linked with Lloris when news of his availability first broke, in recent days Tottenham, and new manager Andre Villas-Boas, have emerged as his likeliest suitors.
It is reported that Spurs have been holding talks with Lyon in an effort to sign the goalkeeper, though president Aulas claims a firm offer is yet to be received.
"There is no official offer for Hugo Lloris," Aulas told L'Equipe.
Aulas added that if Spurs do not firm up their interest prior to Lyon's July 15 deadline then, "he will stay and everyone will be happy."
The Lyon president also stated that he has held "serious discussions" with Premier League clubs regarding the possible transfer of left-back Aly Cissokho.
The 24-year-old has been linked with Liverpool recently.