Former President Donald J. Trump said on Wednesday that he would hold a rally this month at Madison Square Garden, part of his campaign’s efforts in largely Democratic states.

“We just rented Madison Square Garden,” he said at a rally in Scranton, Pa., eliciting cheers. “We’re going to make a play for New York.”

Mr. Trump has repeatedly claimed that New York is in play this election, despite few polls indicating that the state could swing red.

Manhattan is among the most Democratic counties in the country, and a Republican presidential candidate has not won it in a century. Ronald Reagan was the most recent Republican presidential candidate to carry New York State, during his 1984 re-election campaign.

Mr. Trump’s campaign has not yet announced a date for the rally, but The New York Post reported that it would be held on Oct. 27, less than two weeks before Election Day. The Garden, the home of the New York Knicks and the New York Rangers, can seat around 20,000 people depending on the arena’s configuration. It has yet to host a presidential candidate this year.

During his remarks in Scranton, Mr. Trump also said he hoped to rally in arenas in New Jersey and Atlanta, most likely referring to the Prudential Center in Newark, N.J., and the State Farm Arena in Atlanta.

“We’re doing arenas because the crowds are so big,” Mr. Trump said.

In a noticeable campaign difference from Ms. Harris, who has largely rallied in swing states, Mr. Trump often holds rallies in places rarely considered battlegrounds. This year, Mr. Trump has held campaign rallies in New Jersey and Montana, and, in New York, he has rallied in the South Bronx and on Long Island.