Cheap-chic retailing can count another international player in the US — and it’s now eyeing Manhattan.

Last week, the Ireland-based Primark opened in Boston in the historic Filene’s building at Downtown Crossing. Sources say that the retailer, which promises “amazing fashion, amazing prices,” has Gotham in its sights.

“They are going to look for a prime building that has exposure that is similar to H&M’s major locations,” said a source who requested anonymity.

But one hiccup for Primark is its focus on West 34th Street, which for now doesn’t have the large swath of space — some 70,000 square feet — that the retailer desires.

Fans who want to check out its goods sooner will be able to take a jaunt to the Staten Island Mall, where Primark in 2016 will open in space leased from a giant Sears store.

Meanwhile Primark is “looking at the I95 corridor,” a spokeswoman told The Post.

As The Post previously reported, Primark has already cut deals to lease space from Macerich as well as Sears. In September, Primark opened a distribution center in Bethlehem, Pa., and will debut at King of Prussia Mall, also in Pennsylvania, on Nov. 25, 2015.

In 2016, Primark will open at the Burlington Mall and South Shore Plaza Mall, both in Massachusetts, the Danbury Fair mall in Connecticut, the Freehold Raceway Mall in New Jersey, and the Willow Grove Park Mall in Pennsylvania.

Founded in 1969 in Dublin, Primark has 292 stores and employs more than 62,000 people in the eurozone and US.

Voice judge and pop star Christina Aguilera has checked out a $105 million apartment in her own Tribeca ’hood.

Our spies spotted the blond bombshell touring the topmost, 25,000-square- foot penthouse at 100 Barclay St. — which isn’t even on the market yet, according to the building’s Web site.

As we first told you, Ben Shaoul of Magnum Real Estate purchased the top of the Ralph Walker-designed Verizon Building at 140 West St. — so he could reconfigure the space into family- friendly apartments with Barclay Street entrances.

The building and the penthouse have numerous set-backs that will be used for terraces and amenity spaces.

Aguilera has a $10 million home in Beverly Hills and two children, a boy, Max, with her first husband, Jordan Bratman, and a girl, Summer, with her fiancé, Matt Rutler.

A decade ago, Aguilera was “miniaturized” for a Verizon V Cast commercial that bragged about the first broadband-quality videos on its smartphone. And two years later, her hit “Candyman” was used to promote the Verizon Wireless LG Chocolate phone.

Shaoul declined comment through a spokeswoman who was unaware of the visit, and Aguilera’s rep did not respond prior to press time.

Between Yom Kippur atonement and the Pope’s visit this week, real estate charity is booming.

Eric Trump’s 9th Annual ETF Golf Invitational & Auction Dinner — with a performance by Gilbert Gottfried and hosted by Elvis Duran — on Monday achieved a golf-event record of $1.7 million for St. Jude Children’s Research Hospital. The sum counts toward the $5 million the foundation plans to raise this year.

For a second year, Matthew Schmeelk of Kensington Vanguard National Land Services, Arvind Chary of Atlas Real Estate Partners and Daniel Rudin of Angelo, Gordon & Co. are rounding up commercial real estate executives for a sleepover-in-the-street at Covenant House in both New York and Los Angeles on Oct. 8th with a goal of raising $300,000 this year.

Last year, during breakout discussions with residents, a young Covenant House occupant asked Rudin about his first job, in a coffee shop in Minnesota.

The teen’s eyes widened and he told Rudin, “I work at a coffee shop right now.” “He realized it doesn’t mean he can’t aspire for a better job,” Rudin said. “The experience I had last year was completely moving.”

Also, the New York Building Foundation, the philanthropic arm of the New York Building Congress, has provided $15,000 to Sanctuary for Families to expand its Economic Empowerment Program to include an internship.

And finally, the Intrepid Fallen Heroes team biked six days, 14 hours and 39 minutes to win the grueling 3,000-mile Race Across America while raising more than $640,000 for the Intrepid Fallen Heroes Fund.

The team included Winston Fisher of Fisher Brothers, Evan “Chip” Marks of Sungate Asset Management, Brian Collins of Fisher Brothers and Jessica Lynn Marino of Instinet.

Mazel tov.