It is understood that the 23-year-old is on the Gunners' shortlist but contrary to reports in France, they are yet to make a firm bid this summer.
That is at least in part because Arsenal are looking to overhaul their midfield options and need to move existing players on before pursuing other targets.
Matteo Guendouzi has joined Marseille in an initial loan deal which is expected to become permanent while the club are in talks over Granit Xhaka's move to Roma and are also open to offers for Lucas Torreira.
The Gunners are in advanced talks to sign Albert Sambi Lokonga from Anderlecht -- with the two clubs are thought to be on the brink of agreeing a fee of around £15m plus add-ons -- but any further outgoings would help generate space funds for a move to sign Aouar.
Sources have told ESPN that Lyon would be willing to accept a fee in the region of €25m. It is also claimed that the Gunners are likely to face competition from several clubs including Paris Saint-Germain and an unnamed Spanish team.
However, Aouar, who has two years remaining on his contract, is thought to be open to a move to the Premier League and would not rule out a move to Arsenal on the basis they cannot offer European football.
Lyon's valuation of Aouar has dropped considerably from last year when Arsenal first expressed serious interest. The Ligue 1 side were demanding €60m but the Gunners made one offer of €35m which was rejected.
Sources told ESPN in January that Aouar was surprised Arsenal did not make more of a concerted attempt to sign him and at that time he was eager on a move to Barcelona or Real Madrid.
However, it appears interest from those clubs is yet to materalise at this stage and Arsenal may have an opportunity to complete a deal for a player who made 33 appearances for Lyon last season, registering eight goals and four assists, as they missed out on Champions League qualification by two points, finishing fourth in Ligue 1.