Liverpool retain a strong interest in the 19-year-old France youth international but are seemingly happy to wait for the player to develop in Ligue 1 before making an attempt to sign him, according to French radio station RMC.
Aouar, 19, made his first-team debut for Lyon in 2017 and established himself as one of Ligue 1s bright young talents over the course of last season.
Barcelona have previously also reportedly expressed an interest in a deal for the teenager.
Speaking in May, Aouar downplayed the speculation linking him with Europes top sides and maintained he needed to continue his development at Lyon.
He told France Football: Im well protected with my family. Its nice to hear, but Im not getting carried away. My feet are firmly on the ground.
Ive only got a good half-season behind me, and I have everything to develop at Lyon.
Liverpool have also been heavily linked with Aouars more established Lyon teammate Nabil Fekir in a reported £70m deal.
Fekirs agent, Jean-Pierre Bernes, dismissed the suggestion he was due to meet Liverpool to finalise negotiations last week.
A deal for Liverpool to sign the France international is far from certain, but reports have suggested a move could gather pace following the World Cup.