De Telegraaf reported earlier on Tuesday that Netherlands forward Depay was set to join compatriots Frenkie de Jong and Ronald Koeman at Barca this week in a transfer worth 25 million euros ($29.6 million).
Responding on Twitter, Aulas said: “The president of Barcelona told me on Sunday that Barca are really suffering from the Covid crisis and were not able to make an offer.”
Koeman has been on the hunt for a striker after telling Uruguayan Luis Suarez he wasn’t in his plans for the coming season.
Depay played an important role in Lyon’s progress to the Champions League semi-final and scored a hat-trick in their opening Ligue 1 win of the season over Dijon.
However, he had announced that he did not wish to extend his Lyon contract, which expires next summer, and has never hidden his desire to play “for a bigger club”.
The 26-year-old started on the bench for Lyon’s Ligue 1 match against Montpellier on Tuesday night.
He began his career with PSV Eindhoven before moving to Manchester United and, in 2017, Lyon.