Arsenal's first offer of €35 million was rejected by Lyon on Friday but the two clubs are still in negotiations for the 22-year-old France under-21 international.
The French side value him at €60m but are ready to accept around €45m with bonuses. The London club are ready to increase their offer and are optimistic an agreement can be reached.
Lyon have agreed a deal with AC Milan to sign their Brazilian playmaker Lucas Paqueta for around €20m. Paqueta, 23, has been earmarked as being Aouar's replacement if the Frenchman was to leave the club.
Aouar is Arsenal manager Mikel Arteta's priority this transfer window ahead of other targets such as Thomas Partey from Atletico Madrid, who has a release clause of €50m.