Madison Square Garden Wants to Stay Put Forever. It May Not Be So Easy.

For the basketball players navigating a last-second play at Madison Square Garden, even for the musicians in its owner’s band, JD & the Straight Shot, timing can mean everything.

And so it might for Madison Square Garden itself, which earlier this month quietly told city officials it would seek a permanent permit to host big shows and games at its location atop Penn Station.

New York City law requires arenas with more than 2,500 seats to get special permits to operate, though land-use peculiarities have exempted many city venues from those requirements, including Yankee Stadium and Barclays Center.

A decade ago, city lawmakers denied the Garden’s request for a permanent permit, and instead granted it a 10-year license — far shorter than the 50-year permit it had just held. Lawmakers urged the Garden’s owner, MSG Entertainment, to use that time to find a new home for the arena.

That never happened. Now, with the Garden’s current license set to expire in July, its push for a new permanent permit seems to come at an inopportune time.

In December, it was reported that MSG Entertainment was using facial recognition at its venues, including the Garden and Radio City Music Hall, to ban lawyers whose firms were suing Madison Square Garden, regardless of the size of the firm and whether the attorneys had any relationship to the litigation in question. In one case, a lawyer taking her daughter’s Girl Scout troop to see the Rockettes at Radio City was prohibited from entering the venue.

Last week, after the State Liquor Authority said it was investigating the Garden to see if it was violating the terms of its liquor license, MSG Entertainment’s chief executive, James Dolan, appeared on Fox 5 and challenged Sharif Kabir, the authority’s top executive.

Mr. Dolan suggested that the Garden’s management would “pick a night, maybe a Rangers game, and we’re going to shut down all the liquor and alcohol in the building.” He then held up a flier with Mr. Kabir’s photo and contact information, so that fans might “tell him to stick to his knitting.”

And in a personnel move that might be unpopular with the city’s Democratic leaders, Mr. Dolan hired Hope Hicks, Donald J. Trump’s former communications director, as a consultant, a development reported on Tuesday by The Daily News. (Mr. Dolan spent hundreds of thousands of dollars to help elect Mr. Trump as president during his 2016 campaign.)

Those issues are not central to the new permit application, but they are likely to further antagonize officials and urban planners who already believe that the Garden is treated far too leniently by the city and state. The arena is the beneficiary of $43 million in yearly property tax breaks and has for years been an obstacle to renovating the nation’s busiest rail station, which lies beneath it.

“It’s very difficult to fix Penn Station with the Garden sitting on top of it,” said Vishaan Chakrabarti, an architect who has drawn up plans for a new Penn Station. “And anyone who thinks otherwise should look at Grand Central Terminal and imagine what it would be like to have a 20,000-seat sports arena sitting on top of it.”

“Anyone can or should be able to go to this arena,” said Alexandros Washburn, the former chief urban designer at the Department of City Planning who is now working with the Grand Penn Community Alliance in support of a complete renovation of Penn Station to restore it to its former grandeur. “It has a public tax break. It has a public special permit. It uses public infrastructure. So we have to understand that it is a public facility.”

On Jan. 13, Madison Square Garden began the process of seeking a new so-called special permit, according to a notice posted on the Planning Department’s website.

Like the last go-round, the arena is seeking to renew the permit in perpetuity, according to two city officials briefed on the request, a fact confirmed by Mikyl Cordova, a Garden spokeswoman.

“We will be filing Madison Square Garden’s special permit application in the coming weeks,” Ms. Cordova said. “We will share more details at the appropriate time and look forward to participating in the special permit process to ensure the Penn Station area is a more welcoming environment.”

In order to get a new special permit, the Garden will have to survive a monthslong gauntlet of public reviews, culminating in a vote by the New York City Council.

Brad Hoylman-Sigal, the state senator whose district encompasses the arena, expressed hope that the Council would use the expiration of the Garden’s 10-year permit as a lever to extract concessions from Mr. Dolan, including on its use of facial recognition technology.

“As the Council reviews the special permit, I hope they consider issues like the use of biometric surveillance and denying fans entry into the Garden, just because they happen to work for a law firm that represents clients perceived as hostile to Jim Dolan’s financial and legal interests,” Mr. Hoylman-Sigal said.

The move is also likely to renew conversations about the wisdom of allowing Madison Square Garden to remain at its current location, where its presence has complicated efforts to renovate Penn Station. Related Companies, the developer of Hudson Yards, has proposed relocating the Garden to the Far West Side of Manhattan, a move Mr. Dolan opposes.

Traditionally, the Council defers to the local member on land-use issues. Erik Bottcher, the councilman whose district encompasses the Garden, suggested that the Council should take advantage of a “one-time opportunity for a new, state-of-the-art arena at the Western Rail Yard that could set a new standard for the world.”

“New Yorkers deserve a first-rate entertainment and sports arena, and a first-rate train station, and moving Madison Square Garden to the Western Rail Yard would achieve both,” Mr. Bottcher added.

The last time the city grappled with the question of Madison Square Garden’s special permit, urbanist groups had coalesced around the idea that the arena had to move to make way for a new and better Penn Station.

Since then, the political will for relocating the Garden seems to have ebbed. The state is setting its hopes on a contested new plan to allow 10 skyscrapers to be built around Penn Station that would, officials argue, generate enough revenue to help repair the station.

“My thinking on that has changed quite a lot,” said Tom Wright, chief executive of the Regional Plan Association, which rallied behind evicting the Garden a decade ago. “I really do believe we can get a really great Penn Station without necessarily moving the Garden.”

Ms. Cordova dismissed any discussion of relocation.

“To date, there have been no substantial conversations about moving the Garden since the city granted the last permit 10 years ago,” she said. “In fact, no realistic proposal or financial model for moving the Garden has ever been presented and, according to Empire State Development, any plan to relocate the Garden would cost the city and taxpayers an estimated $8.5 billion — an unfathomable figure better used for the city’s many other priorities.”

(Ms. Cordova was citing a state-generated estimate for what it would cost to buy out the Garden that included more than $2 billion for reconstructing Penn Station.)

For their part, city officials are planning to tie a new zoning amendment to the special permit process that would require improvements to the public space around the arena, including better pedestrian access.

“We need to make sure that the continued operations of the arena will be complementary to the redevelopment of Penn Station, and enable real improvements to the public realm,” said Dan Garodnick, director of the Planning Department. “We will be evaluating the proposal in this context.”