The Gunners appeared to be at the front of the queue for the Frenchman during the summer transfer window, only for a move to break down due to failing to agree a fee.
While Mikel Arteta's side have struggled to net in the Premier League, the 22-year-old has contributed three goals and three assists in Ligue 1.
According to Italian journalist Fabrizio Romano, club officials feel that the playmaker is the right player to add creativity to the current squad.
Speaking on the Feather on Football Podcast, Romano claimed that Arsenal would need to pay €60m (£53.3m) to tempt Lyon into a sale.
Lyon currently hold a one-point lead at the top of the Ligue 1 standings, making it highly unlikely that Aouar would leave in January.