Gunners manager Arsene Wenger is reportedly interested in signing his compatriot, but the north Londoners could face competition from Liverpool and Tottenham
Several English sides have been linked with the 25-year-old shot-stopper, with Arsenal said to be particularly keen, but Aulas claims that nobody has made an approach for the player.
"Lloris told me that he would like to leave if he has an opportunity to play for one of the five biggest European sides," the Lyon supremo told his club's official website.
"If any of these teams make an offer meeting his market value, €20m, he will be allowed to leave.
"For now, though, I have not received any offers, neither from Arsenal nor from elsewhere."
Lloris, who represented Les Bleus at Euro 2012, joined Lyon from Nice in 2008 for a reported fee of €8.5 million.