New York City Mayor Michael Bloomberg and presumptive GOP presidential nominee Mitt Romney met Tuesday morning for breakfast, according to multiple media reports.

The meeting, which was the first between the two, took place at the Bloomberg Foundation offices on East 78th Street.

The Republican-turned-independent mayor has been occasionally mentioned as a potential third-party presidential candidate due to the billionaire's ability to self-fund and his centrist positions. He did not endorse in 2008, but The New York Times reports that he is said to be open to the idea of endorsing a candidate.

Bloomberg and President Barack Obama met sometime last winter and discussed the mayor's future, according to The New York Times. His third term ends in 2013.

Bloomberg's positions on gay marriage, gun control and reproductive rights are to the left of Romney's. On the other hand, Bloomberg said in September that Obama's Buffett Rule -- which would have required those who earn more than $1 million to pay 30 percent of their income in taxes -- is "just theatrics."

Romney is marking the anniversary of the Osama bin Laden raid on Tuesday with former New York City Mayor Rudy Giuliani, who endorsed him last week, at a New York City fire station.

UPDATE: 2:25 p.m. -- During a press availability with Giuliani, Romney said that he and Bloomberg had a "very nice" meeting.

"You have to look at what New York has done under this mayor and under Mayor Bloomberg and say the city is just a remarkable place doing a superb job, from everything he reported," Romney said.

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