Condé Nast gluttons eager to chow down at Eataly, the Italian gourmet mega-market due to open at 4 World Trade Center, will have to settle for nearby Majestic Pizza for a while.

A dispute between the Port Authority and WTC mall operator Westfield has held up Eataly’s access to its 41,000- square-foot floor.

While it’s unclear who’s at fault, Westfield has balked at taking the keys from the PA, according to multiple sources. Until Westfield takes possession, it can’t turn retail space over to Eataly — which will be close to Condé Nast’s 1 WTC offices — or other tenants.

The untimely impasse makes it increasingly questionable whether hotly awaited Eataly and other retailers in the complex will have time to open their doors this year. Westfield also has signed leases with Michael Kors, Turnbull & Asser, John Varvatos and restaurateur Daniel Boulud, among others.

The PA “gave access” two months ago to Westfield for Eataly and other stores inside 4 WTC and underground corridors — although not to the unfinished train station “Oculus. But until Westfield signs off on the handover, tenants can’t start construction, much less move in, sources said.

Officials and reps for both the PA and Westfield declined to comment.

However, an insider said, “PA contractors are waiting for Westfield to sign off on the work or come back with a punch list — but so far the PA is still waiting. Meanwhile, Westfield is telling retailers the delay is due to the PA.”

The PA only just began installing glass for the “Oculus” roof of the Santiago Calatrava-designed Transportation Hub, and it can’t turn the vast hall over to Westfield until that job’s done later this year. But it was unclear whether the timing has anything to do with Eataly, far removed from the Hub.

The mystery of when Eataly will open is just part of WTC retail buzz, which includes the tale that Calatrava, who visited the site Wednesday, once playfully threw an iPhone at Apple staff during an argument about design changes Apple wanted made for a possible store in the Oculus.

Westfield said last December that it would “probably” launch the WTC’s total 350,000-square-foot store and restaurant sections in the second half of 2015. It’s since backed off the idea of holding a grand opening for the whole megillah, saying it “is expected to open in stages from 2015.”

Eataly signed a lease one year ago, and was expected to open on 4 WTC’s third floor this year.

Owners Mario Batali and Joe Bastianich are itching to start work in what’s now raw space. Eataly rep Cristina Villa said, “We are patiently awaiting our turn in a very complicated project.”

In fact, sources said the Eataly team has weighed possible legal action — which could complicate things more, as Eataly also has a lease to open in Westfield’s Century City mall in LA.

Eataly spokesperson Villa would only say, “We don’t have possession of the space and construction hasn’t begun yet.”

Westfield and Apple are also said to have had talks about a 20,000-square-foot two-level store in the Oculus. A story that Calatrava objected to having a giant glass apple suspended from the 160-foot-high ceiling — the incident that sparked the alleged iPhone toss — could not be confirmed.

Westfield Group paid the PA $1.4 billion for all of the WTC’s retail space.