Swiss-born “Catwoman” Jocelyn Wildenstein is off the market now that she’s engaged to Canadian-born fashion designer Lloyd Klein — but her sprawling Trump World Tower apartment is about to be back on it.

Wildenstein, a socialite who now sports a massive 32-karat diamond engagement ring, is listing the 5,160-square-foot spread at 845 United Nations Plaza for $11 million, Gimme Shelter has learned.

It last asked $12.9 million with a different broker earlier this year.

Wildenstein gets her “Catwoman” moniker from the millions of dollars she reportedly spent on plastic surgery procedures, including canthopexy — which gives the recipient’s eyes a cat-like appearance.

Now a grandmother, she has dated Klein — who has dressed divas from Nicki Minaj to Joan Collins — for the past 14 years. Last December, they were arrested following a, well, catfight that left them both scratched up.

It was a “one night” domestic fight, the couple told the Daily Mail, and, they said, it left them more enamored with each other than ever before.

This month, however, it was reported that Wildenstein had defaulted on a $4.5 million mortgage for this unit.

The unfinished apartment is actually a combination of three separate units that have been joined and gutted. It sports five bedrooms, 4 1/2 bathrooms and stunning views that include the East River, the Empire State Building and the Chrysler Building.

“We opened up all the apartments into one and left the space totally raw,” says listing broker Khashy Eyn, CEO of Platinum Properties. “We figured that when people are spending this kind of money, they want to create their own custom home. Whoever buys this can make it into exactly what they want at a fraction of paying for a finished apartment that they would end up gutting anyway.”

Eyn adds, “It’s an apartment in the sky with airplane views.”