"It would be a wonderful thing," Carson said on Fox Business, arguing a debate would help Trump contrast his ideas from those of Sanders, a self-described democratic socialist.

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"I would love to see such a debate because it would help to crystalize for the American people the difference between traditional American values and socialism," Carson said.

Buzz surrounding a possible Trump-Sanders debate has escalated two days after Trump expressed openness to such an event in off-the-cuff remarks on a late-night talk show.

Sanders, who has pushed for a Democratic debate in California ahead of the June 7 primary, took up Trump on the idea. Trump later said at a news conference that he'd want millions donated to charity for such an event.

"The problem with debating Bernie is he's going to lose," Trump remarked while speaking to reporters in North Dakota, toying with the idea of taking on the Independent Vermont senator one-on-one.