Fekir, who is currently with the France squad at the 2018 World Cup, scored 23 times and registered eight assists in 40 appearances for Lyon during an impressive 2017-18 campaign.
The 24-year-old saw a move to Liverpool break down earlier this summer amid suggestions of a problem with his medical, but the Reds are still believed to be interested in a move.
Aulas, however, 'thinks' that Fekir will stay with Lyon entering the 2018-19 campaign.
"I think that Nabil will be at OL next season," Aulas told RMC Sport. "I have almost a father-son relationship with my players, I gave him the chance to go to Liverpool because it was his dream club.
"I did that too with [Corentin] Tolisso and [Samuel] Umtiti, he is our captain and it is the coach's wish to keep him."
Fekir has played 58 minutes of football for France at this year's World Cup. body check tags ::