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The striker looked set to move to Spain in a deal costing Barcelona in the region of €25-30 million, various reports indicated.
Yet the deal now looks to be off, withAulas declaringBarcelona president Josep Maria Bartomeu personally told him the Catalan giants were in no position to make an offer.
In a Twitter message, Aulas pointed to a report from Dutch newspaper De Telegraaf that suggested a €30m (£28m/$36m)move for the 26-year-old was in the offing.
Aulas wrote: "The president of Barca indicated to me on Sunday that Barca were suffering a lot from the Covidcrisis and didn't have the possibility to make an offer. #memphis"
Bartomeu recently said Barcelona faced losing around 30 per cent of their budgeted income because of the coronavirus pandemic, with that figure likely to equate to somewhere close to €300m (£276m/$355m).
The Dutch international was asked about Barca's interest last week and confirmed that the Catalan side were keen to bring him in.
"I haven't heard much more from my agent. I know that there is interest, but I don't have much more to say because I don't know much about it."
Should Barca be unable to make an offer for Depay,Aulashas previously claimed that Roma are also keen on the forward.