Some moderate Republicans are in talks to come up with a bipartisan solution as the battle over who will be the next House speaker drags on.

"There are informal conversations that have been underway. When we get back to Washington tomorrow, it’s important to begin to formalize those discussions," House Minority Leader Hakeem Jeffries said during an appearance on NBC’s "Meet the Press" on Sunday.

The comments come as House Republicans have been locked in a chaotic battle for the last two weeks over the fate of the speakership, with former House Speaker Kevin McCarthy being ejected from the post this month.

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Hakeem Jeffries, Kevin McCarthy split

House Minority Leader Hakeem Jeffries, left, and former House Speaker Kevin McCarthy (Win McNamee | Kevin Dietsch via Getty Images / File)

Rep. Jim Jordan, R-Ohio, was nominated by a majority of Republicans on Friday but faces an uphill battle in gaining enough support among his GOP colleagues in a floor vote in which all Democrats are expected to oppose him.

The uncertainty has seemingly opened the door for a bipartisan deal, with Jeffries saying the goal of a deal would be to prevent "extremists" from being able to dictate the agenda in the House.

"The current rules of the House have facilitated a handful of Republicans being able to determine what gets voted on in the House of Representatives, and that undermines the interests of the American people. We can change the rules to facilitate bipartisanship, and that should be the starting point of our conversation," Jeffries said.

House Judiciary Chairman Rep. Jim Jordan, R-Ohio, presides over a hearing

Rep. Jim Jordan, R-Ohio, was nominated by a majority of Republicans on Friday but faces an uphill battle in gaining enough support among his GOP colleagues in a floor vote in which all Democrats are expected to oppose him. (Anna Moneymaker / Getty Images / File)

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But such an effort is likely to face major pushback from Republicans if a Democrat were the choice, with even moderates arguing that a vote for a Democrat would be akin to "political suicide."

"No Republican is going to vote for a Democrat," Rep. Bob Good, R-Va., said last week during an interview with Fox Business "That would be political suicide, even for the most moderate of members."

Meanwhile, Rep. Thomas Massie, R-Ky., noted that Democrats already own control of both the Senate and the White House, arguing that Republicans should not give ground when it comes to their control of the House.

Massie of Kentucky

Rep. Thomas Massie, R-Ky. (Tom Williams / CQ-Roll Call Inc. via Getty Images / File)

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"Some Republicans want to cut a deal with Democrat leader Hakeem Jeffries to elect a Speaker," Massie said Sunday in a post on X, formerly Twitter. "With Democrats controlling the White House and the Senate, we must not give up control of the House. Republicans should unite behind Jim Jordan as our Speaker of the House!"