Republican presidential candidate Vivek Ramaswamy and Rep. Ro Khanna, D-Calif., are floating a potential debate in New Hampshire.

The potential showdown was suggested this week after Ramaswamy slammed the Republican National Committee for halting a joint appearance with GOP rival Chris Christie on FOX News' "Special Report" over alleged violation of the GOP debate rules. 

After tech billionaire Elon Musk offered to host a debate on his platform X, Ramaswamy replied, "The RNC won’t let the GOP candidates do it, but I’d go for it with a smart Democrat who’s willing."

"The University of Chicago Institute of Politics wants to have a civil discourse with the two of us on race, identity and the American dream. I accepted. I assume, as a speech advocate, you’re game @VivekGRamaswamy?" Khanna challenged the 2024 hopeful on Wednesday. 

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Rep. Ro Khanna, D-Calif., at rally

Rep. Ro Khanna, D-Calif., challenged GOP hopeful Vivek Ramaswamy to debate him in New Hampshire. (Anna Moneymaker/Getty Images)

Ramaswamy was previously slated to debate independent presidential candidate Dr. Cornel West at the University of Chicago, but the progressive rival canceled due to a scheduling conflict. Ramaswamy surmised that Khanna was called by the university to fill in. 

"You’re a solid dude with whom I disagree on a lot, and I’d be glad to have a discussion at some point, just need to balance it in the context of campaign priorities. If you are willing to do it in New Hampshire, I’m game," Ramaswamy said. 

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Khanna offered to do a "fireside conversation" at St. Anselm New Hampshire Institute of Politics.

"Let’s have a thoughtful discussion & elevate national discourse, instead of 30 second sound bites, shallow answers and name calling," the Democratic lawmaker said. 

Khanna told FOX News Digital, "Our teams are in touch and engaged in a constructive approach to work out the details."

Vivek Ramaswamy at event

Republican candidate Vivek Ramaswamy previously slammed the RNC for quashing his scheduled discussion with rival Chris Christie on "Special Report." ( Eva Marie Uzcategui/Bloomberg via Getty Images)

The potential event comes as one of Ramaswamy's GOP rivals, Florida Gov. Ron DeSantis, is set to square off against Democratic California Gov. Gavin Newsom in a debate on Nov. 30 moderated by FOX News' Sean Hannity

Ramaswamy's campaign criticized the RNC for allowing DeSantis to debate Newsom while quashing his previously scheduled discussion with Christie. 

According to the RNC's debate rules, Republicans candidates agree to not participate "in any non-RNC sanctioned debate for the remainder of the election cycle." 

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Desantis-Hannity-Newsome-Debate

FOX News Channel’s Sean Hannity, center, will moderate a red vs. blue state debate between Republican Florida Gov. Ron DeSantis, left, and Democratic California Gov. Gavin Newsom. (FOX)

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Newsom, notably, is not a declared presidential candidate, despite the buzz he has received as being a potential alternative to President Biden at the top of the Democratic ticket in 2024. He has dismissed the rumors and expressed his support for Biden's re-election multiple times. 

Like Newsom, Khanna's name has also been floated as a potential presidential contender in 2028. 

The latest FOX News poll released this week showed Ramaswamy with 7% support among GOP voters, placing fourth behind former U.N. Ambassador Nikki Haley at 10%, DeSantis at 13% and former President Donald Trump, who maintains a commanding lead at 59%.

Get the latest updates from the 2024 campaign trail, exclusive interviews and more at our Fox News Digital election hub.