The Reds have yet to rule out returning to the table for the Lyon skipper after backing out of a deal at the twelfth hour earlier this month. However, Los Blancos' interest could set off some alarm bells on Merseyside due to a potential bidding war.
Reports suggested Liverpool opted out of finalising Fekir's transfer due to medical concerns, but speaking on French television Aulas declared the collapse arose after he called off the transfer himself because it had dragged on for far too long.
He insists his actions have subsequently brought Real Madrid to the table following the appointment of former Spain manager Julen Lopetegui.
Speaking to RT France, via the Mirror, Aulas said: “Yeah, listen, at that stage it was foreseen he would go to Liverpool, I had given it the green light to go ahead. But it just took too long, things were just too drawn out.
“He is an exceptional player, he keeps the ball in little space and has an incredible talent. The fact that things didn’t conclude with Liverpool and it didn’t happen in that time frame. (He) has peaked the interest of a lot of other clubs - Real Madrid, but not just Real Madrid and their new trainer.
“There is a lot of interest from other camps, so everything is possible.”
Despite the Spanish giants' late interest and the Reds' concerns over issues with a ligament graft he received during surgery on a cruciate ligament injury, Fekir stills hopes a compromise over the terms of payment can be reached between the two clubs.
The 24-year-old still harbours a burning desire to move to Liverpool, and his agent Jean Pierre-Bernes revealed earlier this week that a deal could still happen, despite contrasting reports coming out of both clubs.
The report from the Mirror claims the attacker has a close relationship with Aulas and he will ask him to reconsider making concessions to allow the transfer to receive a green light, although no talks will resume until after the World Cup, leaving Aulas hopeful he will stay in France.
"But at the same time we still have eyes for him staying in Lyon. My objective is to get him to stay - the players are like sons to me and I hope to persuade him to stay," he added.
“But if he absolutely wishes to leave, then we will try to find the biggest club to match his talent."