The Gunners are desperate to bring the French playmaker to north London following his superb displays in Ligue 1 in recent seasons.
The 22-year-old has been heavily linked with a move to the Emirates throughout the summer, with Arteta desperate to add quality to his midfield before the transfer window closes on October 5.
And according to French outlet Telefoot, Emirates chiefs have now officially submitted an offer for the France international.
The report comes just hours after Lyon president Jean-Michel Aulas expressed doubt whether the Gunners have the funds to sign Aouar.
Last week, Aulas said Arteta's side couldn't afford him and he has again once again echoed those sentiments.
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Speaking to Le Progres via GFFN, he said: "Financially, Arsenal are like everyone else (in a tricky spot).
"And Houssem could say to himself that the best thing would be to stay with us."
Meanwhile, midfielder Lucas Torreira has been linked with a move to Atletico Madrid before the transfer window closer.
The Arsenal midfielder is surplus to requirements by Mikel Arteta and has been looking for a move all summer.
Arteta was asked about whether Torreira was any close to leave the Gunners, and he said: "We don't have any update on Lucas or any other player at the moment.
Arsenal have reportedly launched their bid for Lyon playmaker Houssem Aouar.