Lyon finished seventh on the Ligue 1 table after the banning of all sporting activities in France until September led to the abrupt ending of top flight football for the 2019/2020 season.
The decision meant Lyon failed to secure European football for the first time since 1997.
Technically, Lyon can still qualify for the Champions League if they win this season’s competition, as they held a 1-0 first leg lead over Juventus in the round of 16 before football was suspended.
Depay has revitalized his career in France following a forgettable spell with Manchester United in the Premier League.
The 26-year-old’s contact expires next summer but Lyon are bent on securing an extension for their club captain, who has started courting interest from some of Europe’s best clubs.
Speaking to Le Progres, Aulas said: "I'm going to do everything to keep the players.
"But players programmed to play European competitions may want to look elsewhere because we are deprived of the Champions League.
"I have no news for now. Memphis tells me that he is ready to discuss [a new contract] when he returns.
"His agents say that he is more thinking about the possibility of departing if we don’t have European football."
Depay is currently sidelined with a serious knee injury that would have kept him out of action for the remainder of the 2019/2020 season and also miss EURO 2020, which has been postponed to next year.
Depay scored 14 goals in 18 games before getting injured.
