Barca was heavily linked with a move for Depay after former Netherlands boss Ronald Koeman took over in August, but the ex-Manchester United forward remained at the Ligue 1 side.
The Catalan giant is said to be looking to step up its efforts to sign the 26-year-old after Ansu Fati was ruled out for around four months with a knee injury.
Depay's contract with Lyon is set to expire in June and club president Aulas insists he will not be allowed to depart beforehand.
"Memphis is an exceptional player. It is him who is pulling the club, along with a number of other players," Aulas said.
"I was the first to say he would not go to Barcelona. Nobody listened to me during the transfer window because everybody thought he would leave.
"From the start, I told you, they will not leave because in a year when we were unfairly deprived of European competition, we absolutely have to make a success of the season. So, he will stay."
Depay has continued to perform in Ligue 1 despite failing to complete his move to Barca.
He has been involved in eight goals (five scored, three assisted) in the top flight this season, a tally that can only be bettered by Paris Saint-Germain star Kylian Mbappe (seven scored, four assisted).
Furthermore, no player has created more chances in Ligue 1 than Depay, who has a league-leading 27 alongside Leo Dubois.
Depay has set up 35 league goals since his Lyon debut on January 22, 2017, level with Angel Di Maria for the most in the division in that time. Mbappe (110) is the only player to have been involved in more goals than the Dutchman (83) in the same timeframe.