Republican presidential candidate Ben CarsonBenjamin (Ben) Solomon CarsonGillibrand introduces bill blocking HUD rule on undocumented public housing residents Housing authorities raise concerns about Trump plan to evict undocumented immigrants Moulton confirms he'll miss first Democratic debate MORE says he's willing to consider being Donald TrumpDonald John TrumpConway defends herself against Hatch Act allegations amid threat of subpoena How to defuse Gulf tensions and avoid war with Iran Trump says 'stubborn child' Fed 'blew it' by not cutting rates 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.