Swift, one of the most successful musicians of all time, and three-time Super Bowl champion Kelce announced their engagement in August. Speculation has swirled about when and where the pair would get married.
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, the Times said, citing three people with knowledge of the matter.
City Hall spokesperson Dora Pekec confirmed to Reuters that a permit with those details had been filed.
Several members of Kelce's football team, the Kansas City Chiefs, have booked hotel rooms for dates around July 3 at the Marriott Marquis hotel in Times Square, the paper said.
Two sources told the paper the plan called for an intimate gathering of about 100 people at the Garden on July 2, and about 1000 on July 3 for a "splashier celebration, with possible stage appearances."
Winick Productions, an event planning company, filed an application with the city's Street Activity Permit Office in early June, the newspaper said.
The company requested authorisation to set up a tent or canopy outside the arena for the event, which it said would include 500 to 999 attendees, according to the report.
Reuters could not immediately confirm that the wedding would take place in July.
Representatives for Swift, Madison Square Garden and Winick did not immediately respond to a request for comment.
Last week, New York Mayor Zohran Mamdani suggested Swift's wedding would take place soon.
"We are used to big events, and we are incredibly excited for this one. We know it coincides with the Knicks Finals run. We know it coincides with July 4, America 250, Taylor Swift's wedding all happening at the same time. And we are so excited to welcome the world here," he told journalists, referencing the 250th birthday of the United States and basketball championship.
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