Lacazette was expected to join Atletico Madrid earlier this month until the Court of Arbitration for Sport's decision to uphold a summer-long transfer embargo on Los Rojiblancos.
Speaking on Tuesday evening, Aulas told Canal Plus that the 26-year-old is likely to stay with the club for a ninth season.
The Gunners have been linked to the likes of Alvaro Morata and Kylian Mbappe, with strengthening of their strikeforce required, along with the questions surrounding the futures of Alexis Sanchez and Olivier Giroud.
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In an interview with the French broadcaster, Aulas said: "I do not think that Alexandre Lacazette will leave this summer".
The options? "It'll either be a France global or a player from a very big European club".
Aulas confirmed Lyon's interest in Giroud on Wednesday, describing him as "one of the players who might interest us", but doubted whether the player himself would be willing to leave Arsenal. "If there are arrivals at Arsenal, perhaps Olivier would like to return to France".
The striker's impressive form with the Castilla side last campaign, scoring 27 goals, alerted Europe to his potential and now Lyon have opted to sign Diaz.
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