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Mr Trump was on Saturday fielding questions while meeting with a group of officers of the New York Police Department and firefighters to commemorate the attacks on the World Trade Centre.
“If you decide not to run for president, if you decide not to, would you consider running for mayor of New York City?” Mr Trump was asked.
“Well, that’s an interesting question,” he replied in a mock tone, amid laughter. “I would love that. We could straighten it out,” he added.
“I'd say, ‘Fellas, good luck, go to town’. They'd be announcing in one week, ‘There's no crime in this city’.”
New York’s current mayor Bill de Blasio has been facing low approval ratings and is unlikely to run again in November over term-related restrictions.
Despite not making a formal announcement, Mr Trump has kept the door open for his presidential run in 2024 through crowdfunding and rallies. Mr Trump's team had over $100 million in hand, with over $82 million raised in the last six months.
He had a positive response on hand, when asked if he would run for president again.
“Oh, that's a tough question,” Mr Trump said.
“Actually, for me, it's an easy question. I know what I am going to do. But, we are not supposed to be talking about it yet from the standpoint of campaign finance laws, which frankly are ridiculous if you want to know the truth. But we have to live with it. But I think you're going to be happy,” he added.
Several of Mr Trump’s allies, including Republican senator Lindsey Graham, had earlier hinted he was going to run again in 2024.
Once a New York native, Mr Trump shifted his residency to Florida, where he now lives in Palm Beach at his Mar-a-Lago resort with his wife Melania and 15-year-old son Barron.
In a prerecorded statement screened on Saturday at the National Mall in Washington DC, he said: “As a lifelong New Yorker, it was extraordinary to witness the strength and resilience of people of that incredible city and it is indeed an incredible city.”