The Garden is a venerable arena that has hosted all sorts of venues.
But now some would like to see it have a change of venue.
"Madison Square Garden almost moved a couple of years ago," said Manhattan Borough President Scott Stringer.
"We almost had a deal, but it collapsed. Now I want to revive those discussions."
Stringer is calling for MSG's special use permit with the city, put in place 50 years ago and now expired, to be limited to 10 years.
He says moving it to another location would allow for much-needed improvements to an aging Penn Station.
"We can't expand the transit system, so we're stuck as a city because the Garden is sitting on top of our busiest transportation hub," Stringer said.
The Madison Square Garden Company in response claims other special permits don't have artificial expirations.
It also points to having invested $1 billion in new construction in the arena.
And it believes the Garden "is unfairly singled out because of a decision that was made 50 years ago to demolish the original Penn Station."
MSG claims the shorter expiration would be a dangerous precedent that would, in its words, "hinder our ability to make MSG and New York City the long-term home of even more world-class events."
Some sites reportedly being looked at include one on 9th Avenue between 31st and 32nd streets, and a second on 9th and 30th.
Both are now very large postal facilities.
A decision on the special permit ultimately falls in another venue: the city council.