The remainder of the top-flight campaign was curtailed last month after French prime minister Edouard Philippe banned sporting events until September due to the ongoing coronavirus pandemic.
Most teams still had 10 matches remaining and positions were decided on a points-per-game basis, which left Lyon seventh.
Lyon could still technically play in Europe next term if they were to win the Champions League and they led their last-16 tie against Juventus 1-0 before the global health crisis meant the return fixture was postponed.
The future of Depay, who has rebuilt his career in Lyon after an unhappy stint at Manchester United, had already been shrouded in doubt and Aulas – who has vowed to do all he can to keep the Netherlands international at the club – concedes he has fears.
Speaking to Le Progres, he 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."