Reports emerged afterwards claiming that Liverpool were spooked by injury concerns over Fekir, which were thrown up during the 24-year-old's medical.
Aulas, though, says he merely got tired of waiting for the transfer to be completed, and has now suggested that Real could swoop for Fekir.
"Nabil was close to Liverpool, I gave the green light on the move.
"It didn't happen because it was taking too much time. Nabil is an exceptional player.
"When the Liverpool move didn't happen, lots of clubs revealed their interest in him, not only Real Madrid and their new coach.
"Everything is possible, but we want him to stay. But if he wants to leave, we will try and find the biggest club in terms of size and efficiency."
Speaking to beIN Sports, Aulas added: "The interest of Real Madrid? I believe it's true. There are no discussions, but I believe that there is interest.
"I've not spoken any more with Liverpool."
Fekir enjoyed a successful 2017-18 season, scoring 23 goals and providing eight assists in 40 appearances for the French club.
The player's agent has since revealed that, despite the breakdown in negotiations with Liverpool, a move to Anfield could still happen .