The Reds continue to be linked with the World Cup winner in what is turning out to be the transfer saga of the summer.
Fekir’s move to the Reds fell through in June after an 11th hour problem relating to his medical.
Since then, Lyon president Aulas has made a host of conflicting statements regarding the midfielder’s future at the club.
And the Frenchman was at it again on Tuesday morning, this time dropping a hint that the Ligue 1 club may be looking to exploit the English transfer window closing early next month.
“In the current context, as a world champion and with a Lyon team with the ambition to do something very good next year, it’s difficult for Nabil to find a much better club,” he told reporters.
“I don’t fear anything.
“If they leave it will be that we’ve found our amount, but we will do everything so that they don’t leave.
“We will surely have a bit of a storm in the week before the end of the English market on August 9.”
Lyon manager Bruno Genesio added: “Since the end of discussions with Liverpool, we’re expecting some upcoming attacks from other clubs, but he’s still here and keeping him is now an option I’m considering.
“We’ll try to resist.”
The transfer window in England will close on August 9 this season, meaning clubs have three weeks less to sign players.
Liverpool recently added their third new addition of the summer, bringing in Stoke star Xherdan Shaqiri.