Donald Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE is meeting with Mitt Romney again on Tuesday, amid an ongoing brawl within his inner circle about the 2012 GOP nominee's suitability to be secretary of State.

Along with Romney, whose meeting was revealed in a transition team conference call on Monday morning, the president-elect will be meeting with other contenders for the high-profile post.

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Trump is meeting Monday afternoon with former CIA Director David Petraeus, who is also believed to be in the running to head the State Department. Petraeus resigned and pleaded guilty to misdemeanor charges after sharing classified documents with his biographer, with whom he was having an affair.

Trump is meeting another potential top contender on Tuesday: Sen. Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (R-Tenn.), who chairs the Senate’s Foreign Relations Committee and has been loyal to Trump throughout his campaign.

But it's the Romney meeting that will raise eyebrows. Kellyanne Conway, Trump's former campaign manager, has been attacking Romney publicly, saying he's been disloyal and suggesting he couldn't be trusted for the position. Other conservative leaders, including Brent Bozell, have been weighing in to try to stop Trump from appointing Romney.

The former Massachusetts governor was a vocal critic of Trump during the presidential campaign, going so far as to give a speech slamming his candidacy and saying his foreign policy would "make America and the world less safe."

“Donald Trump is a phony, a fraud,” Romney said in Salt Lake City in March. “His promises are as worthless as a degree from Trump University. He's playing the American public for suckers. He gets a free ride to the White House, and all we get is a lousy hat.”

Trump loyalist and former New York City Mayor Rudy Giuliani is himself publicly lobbying for the position.

Asked why Trump felt the need to meet again with Romney, spokesman Jason Miller said he needed more time with a man he doesn't know very well.

"The president-elect is really taking these meetings very seriously," Miller said on the Monday conference call. "He wants to make sure that he's making the absolute best decision for all of the different positions where folks may be joining the administration.

"I think he wants to make sure that he's absolutely sure on all of these. And also, too, I think with the case of Gov. Romney, the two quite frankly haven't spent that much time together.

"This gives them a little more time to do so."

Trump is scheduled to meet several other GOP lawmakers on Tuesday, according to Miller. In addition to Corker, Trump will meet House Homeland Security Committee Chairman Michael McCaul (Texas), who wants to be secretary of Homeland Security; Pennsylvania Rep. Lou Barletta Louis (Lou) James BarlettaBottom Line Ex-GOP congressman to lead group to protect Italian products from tariffs Head of Pennsylvania GOP resigns over alleged explicit texts MORE, who supported Trump long before it was popular to do so; and Tennessee Rep. Marsha Blackburn Marsha BlackburnTaylor Swift on National Voter Registration Day: 'We need everyone' Democrats smell blood with new DHS whistleblower complaint Hillicon Valley: Election officials prepare for new Russian interference battle | 'Markeyverse' of online fans helps take down a Kennedy | GOP senators unveil bill to update tech liability protections MORE, who has been a valuable TV surrogate for Trump throughout his campaign.

— Updated at 11:39 a.m.