The highly-rated shot stopper is keen to leave the Stade Gerland as Les Gones continue their summer clear out despite winning the French cup last season and finishing fourth in Ligue 1.
Lloris has been linked with a number of Europe’s top clubs with Gunners boss Arsene Wenger thought to be preparing a £12 million bid for the France international.
However Aulas has told Wenger he has two week window in which to make a play for the 25-year-old’s signature but will have to stump up £16m to prise him away.
“A certain number of players were not good enough last season and will leave or at least be placed on the transfer list,” said Aulas to the club’s website.
“Hugo told me he would like to leave if an offer comes in from one of the biggest five clubs in Europe.
“If one of these clubs makes an offer that matches his market value, in other words 20 million Euros then he can go.
“If there is no offer before July 15 he will remain at the club for the coming season.
“For the moment there has been no offer from Arsenal or anywhere else.”
Meanwhile, Denmark striker Nicklas Bendter is close to finalising a move away from the Emirates Stadium and will join a ‘top club’ in the summer according to his agent.
With reports linking Malaga and Galatasaray with a move the 24-year-old will his representative Tom Brookes claims he will end up at a big side.
“Nicklas is a top striker, who just proved himself at the Euros,” Brookes told Ekstra Bladet.
“I’m certain that he is going to end up at a top club, but I’m not going to be drawn into speculation.”