The midfielder may yet depart Stade Gerland, while Bafetimbi Gomis is now likely to sign a new contract with the club
Premier League side Arsenal are believed to be admirers of the 27-year-old, with reports tipping the club to make a bid before the end of the summer transfer window.
And though Aulas still believes the midfielder will remain at Stade Gerland, he has refused to rule out Gourcuff leaving the club.
Posting on his personal Twitter account, Aulas said: “I do not think Gourcuff will move to Arsenal, but in football anything is possible.”
The France international has made a blistering start to the season, scoring twice in two games to help Lyon to the summit of the Ligue 1 table.
Meanwhile, Aulas also suggested that Newcastle United target Bafetimbi Gomis will sign a new contract with les Gones.
"At the moment he reflects over a one-year extension with the possibility of release next year."