Republican presidential candidate Ben CarsonBenjamin (Ben) Solomon CarsonBen Carson appears to tie allegation against Kavanaugh to socialist plot The Hill's Morning Report — Sponsored by United Against Nuclear Iran — Kavanaugh, accuser say they’re prepared to testify Report: A third of Ben Carson’s appointees have no housing experience MORE says he's willing to consider being Donald TrumpDonald John TrumpHouse Republican threatens to push for Rosenstein impeachment unless he testifies Judge suggests Trump’s tweet about Stormy Daniels was ‘hyperbole’ not defamation Rosenstein faces Trump showdown 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.