One of the biggest events of the summer is still a mystery: When and where are Taylor Swift and Travis Kelce getting married?

Some powerful clues are emerging.

A permit was filed with New York City to close the streets around Madison Square Garden from July 2 to midday July 4 for an event on July 3, according to three people who have knowledge of the matter. Several members of the Kansas City Chiefs have booked hotel rooms for dates around July 3 at the Marriott Marquis in Times Square, according to a person told of the accommodations.

A fourth person, a city official who was briefed on the preparations, said it more bluntly: Madison Square Garden is planning to host the wedding festivities on July 3.

Since Ms. Swift and Mr. Kelce first announced their engagement last August, their relationship has garnered outsize attention. America does not have royal weddings, but the union between, arguably, the biggest pop star in the world and the Chiefs three-time Super Bowl champion comes close.

Winick Productions, a prominent event planning company that has helped produce major red carpet events including at Madison Square Garden, filed an application with the city’s Street Activity Permit Office in early June. The company requested authorization to set up a tent or canopy outside the arena for the event, which it said would include 500 to 999 attendees. It also said that trucks would need space to load and unload materials at the arena.

A representative for Winick Productions, which is based on the Upper West Side of Manhattan, declined to comment when reached by a reporter on Tuesday.

But Amtrak police officers, who patrol the station beneath the arena, have been told to expect a Swift wedding the weekend of July 4.

Such an event would bring a spectacle to Midtown Manhattan in the height of an already busy tourist season. On July 4, the annual fireworks show in Lower Manhattan will be bigger than usual for the nation’s 250th birthday, and a flotilla of tall ships from around the world will sail into New York Harbor. The city has also seen an influx of visitors for the FIFA World Cup, and a game is scheduled on July 5.

People with knowledge of the permit, the hotel bookings and the event planning at the Garden spoke to The New York Times on the condition of anonymity because they were not authorized to speak publicly. A spokeswoman for Madison Square Garden Sports and MSG Entertainment did not immediately respond to requests for comment. A representative for Ms. Swift declined to comment.

The couple and their celebrity friends would surely draw packs of paparazzi and besotted fans to the streets around the Garden, who devotedly follow Ms. Swift’s career and love life and seek clues hidden in her music and social media.

The musician is known for secrecy around her personal life and occasional head fakes. But that secrecy often only intensifies the publicity around her every move as she orchestrates elaborate productions and highly-anticipated reveals.

Tabloid reports initially claimed the wedding would take place on June 13 at a luxury hotel near Ms. Swift’s home in Rhode Island, but Swifties who descended on the seaside enclave that weekend were left disappointed.

Of course Ms. Swift could be undertaking an intricate ruse. But New York City agencies are proceeding with the expectation that a major Swift event will happen on July 3, said the people who have knowledge of the plans.

While the sports arena might seem like an unusual wedding venue, it is popular for lavish events, including the 1974 wedding of the musician Sly Stone.

And there are obvious draws for Ms. Swift: The venue’s highly controlled and windowless environment provides security and privacy, and, with reports of plans for a custom stage, it would be an ideal setting should Ms. Swift or her celebrity friends want to perform. There is a discrete entrance and ramp to the arena that allows black cars to bring celebrities inside.

The couple would also be able to control images coming from the event in a way that would be difficult to do in an open air venue. There has also been speculation that the Garden might not be the site of the actual nuptials. The couple might exchange vows elsewhere ahead of time and could use the venue for a reception.

The New York Post and TMZ reported earlier this month about their plans to hold an event at the Garden. But Ms. Swift is known for subterfuge, and it is possible she applied for permits at multiple locations or could change her mind about the venue.

When the Rhode Island wedding did not materialize, fans turned their attention to the other potential site of New York, where Ms. Swift has a home in Manhattan’s TriBeCa neighborhood. She has professed her love for the city, including in her 2014 hit “Welcome to New York.”

She fueled more speculation when she visited the arena to root for the New York Knicks in Game 4 of the N.B.A. finals, sitting courtside with her friends, the musicians Alana and Este Haim.

A Madison Square Garden wedding, reception or concert could rise to the level of an “electrified Met Gala,” said Todd Shapiro, a Manhattan publicist. Fans could surround the arena like they did during the Knicks games, he said, and New Yorkers should expect heavy traffic and additional police presence.

There are no public events scheduled between June 29 and July 6 — a notable gap in the calendar during the height of touring season that has fanned the flames around the wedding speculation. (The rock group Bon Jovi will perform at the arena on July 7, and any wedding related decorations would need to be removed before then.)

For those well-versed in Ms. Swift’s lore, other clues loom large: She has hosted extravagant Fourth of July parties. And as her most loyal fans know, July 3 could echo her attachment to the No. 3. There was the surprise 3 a.m. edition of her album Midnights, and a reference to “you squeeze my hand three times in the back of the taxi” in her song “New Year’s Day.”

If the event moves forward at Madison Square Garden, city officials say they are ready for the hoopla and potential crowds. Still, a Swift-Kelce wedding event could present logistical challenges.

The city’s police commissioner, Jessica Tisch, recently laid out the packed calendar of summer events that would require additional overtime funding for the police at a budget hearing.

Pointing to July 4 celebrations and the World Cup and the possibility of Ms. Swift’s wedding, which she said she mentioned in jest, Commissioner Tisch said, “Any one of those on their own would be a big deal in New York City. All of them taken together are unprecedented and are going to place unusual, and I would say historic, demands on the New York City Police Department.”

Mayor Zohran Mamdani said recently that the city was prepared to handle the confluence of events and “excited to welcome the world here.”

“It feels like a city that is coming to life,” he said.

Mr. Mamdani, 34, is a millennial like Ms. Swift and Mr. Kelce, who are both 36. At a news conference earlier this month, Mr. Mamdani said he did not plan to attend their wedding.

“I wish them a lovely wedding,” Mr. Mamdani said, adding that he would listen to her song “Only the Young,” a lesser known track about young people finding their voices, “at home on my own.”

Madison Malone Kircher and Katherine Rosman contributed reporting.