Fekir – who was poised to join Liverpool ahead of the 2018-19 season before negotiations broke down amid reported concerns about his knee – has been linked with a move away from Lyon.
The Reds nearly signed the playmaker last summer, only to see a move scuppered at the last minute.
And World Cup winner Fekir – who is contracted until 2020 and scored 12 goals in all competitions this season – has been given permission to leave boyhood club Lyon, where the 25-year-old made his debut in 2013.
"Effectively, Nabil is outside [of the two departures expected], because we have an understanding that he can go," Aulas said following Friday's 3-2 win over Nimes.
"Thanks Nabil for bringing what he brought, we have an understanding to let him go."
Fekir has made 192 appearances for the club, scoring 69 goals in all competitions during his time with Lyon.
In that time, he's become the teams captain while earning 21 caps for France.
It is expected to be a busy off-season for third-placed Lyon, with Tanguy Ndombele, Ferland Mendy, Moussa Dembele and Memphis Depay all attracting interest.
Aulas added: "We will work on making signings. We are going to try to lose as few players as possible. We are also going to strengthen.
"We are quickly going to have it out with [new sporting director] Juninho and [head coach] Sylvinho."