Barneys boss Daniella Vitale is scrambling to avoid a bankruptcy filing — by finding a fashion-minded investor who’s willing to buy the iconic luxury chain, The Post has learned.

Last week, Vitale, who was named chief executive of the swanky retailer in 2017, met with one potential buyer who is “not in the retail business” and who is seen by industry insiders as an “illogical” choice, according to a source close to the situation.

The name of Vitale’s latest prospect couldn’t immediately be learned, but insiders said the desperate meetings are dimming hopes that the storied fashion destination can avoid a second date with bankruptcy.

Investors from Europe and the US have looked at acquiring the century-old retailer in recent months but have been frightened off, according to a source, by the rent at its Madison Avenue flagship, which tripled this year to about $46 million including taxes.

Among those who kicked the tires and passed: Macy’s, Nordstrom, Neiman Marcus and Saks Fifth Avenue’s owner Hudson’s Bay, according to two sources.

“No one will buy that business without Barneys real estate problem being resolved,” said one source who is close to the situation.

Owned by hedge-fund mogul Richard Perry, Barneys has been struggling to pay its expenses as the rent at the flagship has skyrocketed.

As recently as March, Barneys had discussions with its landlord Ashkenazy Acquisition Corp. to give back some of the 10 floors it occupies at 660 Madison Ave., The Post exclusively reported March 27. A week later, Barneys denied the talks. There have been no recent discussions with the landlord to return space, according to a source.

“The landlord would be open to restructuring the lease,” the source said. “But the problem is returning the upper floors won’t save Barneys a lot of money because the ground floor is the most costly.”

In the meantime, Barneys is hemorrhaging cash. Many vendors have recently stopped shipping new merchandise as the company has publicly acknowledged that it’s “evaluating opportunities” to strengthen its balance sheet.

Fashion insiders were startled by a two-day sale in early July that offered online customers a 20-percent discount on rarely marked-down brands like Louis Vuitton, Prada and Gucci. Many took it as a desperate move to raise cash.

“They were putting things on sale like [Christian] Louboutin shoes that don’t get discounted,” said one industry source.

Now many of those vendors have stopped shipping to Barneys altogether, in part because the primary lender who insures their merchandise has stopped underwriting Barneys’ orders two weeks ago.

“We were the last lenders standing,” Hildun Corp. Co-CEO Gary Wassner told The Post.

Barneys has received some fall merchandise this month, Wassner said, but not enough to carry it through the season.

“They have asked us repeatedly to approve orders for vendors,” Wassner said of Barneys, adding that his firm won’t do so “because we have no information [about Barneys finances] and we don’t know what’s happening there.”

Barneys has since hired restructuring advisors including Kirkland & Ellis, according to a source. The retailer suffered $70 million net loss for the fiscal year that ended in February, according to Debtwire.

“In the end its the vendors that will force a bankruptcy,” said Tim Hynes, Debtwire’s head of research.

“We continue to evolve our strategy and business model for the benefit of all of our stakeholders,” Barneys said in a statement, pointing to upcoming store openings at American Dream in New Jersey and at Bal Harbour Shops in Miami Beach, Fla.