Republican presidential candidate Ben CarsonBenjamin (Ben) Solomon CarsonSean Hannity linked to shell companies that spent M on property: report Overnight Tech: AT&T chief takes the stand to defend merger | Facebook keeps most users out of EU data law's reach | HUD reopens probe into Facebook housing ads | Venture capital firms go to bat for cryptocurrencies Overnight Finance: IMF chief warns against US-China trade war | Trump, Abe can't strike deal on tariff exemptions | Republicans push Trump to rescind Gateway funds MORE says he's willing to consider being Donald TrumpDonald John TrumpClinton takes swipe at 'false equivalency' in media coverage of 2016 election Trump asked Netanyahu if he actually cares about peace: report Official: Trump to urge North Korea to dismantle nuclear program in return for sanctions relief MORE's vice president if the businessman wins the GOP nomination.

"I certainly would sit down and discuss it with him," he told Fox Business host Neil Cavuto on Tuesday, the day of the New Hampshire primary.

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But Carson emphasized that he'd only consider running if he and the nominee had "philosophical alignment."

"I would have to have major philosophical alignment with whoever it was," he said. "I would have to have guarantees that I could do some substantial things."

Carson wouldn't say which candidates he would not consider running on a ticket with.

"Rather than get into that, let's say as long as there is significant philosophical alignment, I wouldn't have any problem," the former neurosurgeon said.

Ultimately, Carson said his focus is on his presidential campaign.

"I'm aiming to really change this country in the same way that I came up with new ways to do very complex things that people have been trying to do for a long long period of time, that's what I want to do with this country," he said.