President-elect 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 has narrowed the field of contenders for secretary of State to four candidates, his transition team said Tuesday.

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Spokesman Jason Miller confirmed that former Massachusetts Gov. Mitt Romney (R) and former New York City Mayor Rudy Giuliani (R) are still under consideration.

Miller would not reveal the names of the other two contenders, but it is widely believed that Trump is also considering retired Gen. David Petraeus and Republican Sen. Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE of Tennessee for the job.

Trump and Romney dined in public with Reince Priebus, Trump's incoming chief of staff, on Tuesday night in New York City. It was Romney’s second meeting with Trump about becoming the nation’s top diplomat.

Romney’s consideration for the role, however, has caused turmoil within Trump’s inner circle.

Giuliani, a longtime Trump confidante, covets the job. And Trump’s former campaign manager, Kellyanne Conway, has openly campaigned against the Romney selection, saying it would anger Trump’s base of supporters.

Romney was highly critical of Trump during the campaign, although the two have recently made strides in repairing their relationship.

Miller on Wednesday said Trump is looking for someone “who shares his world-view and who he has good chemistry with.”

“President-elect Trump thought the dinner [with Romney] went very well and thought there was good chemistry between the two,” Miller said. “But the president-elect and Gov. Romney have not spent a significant amount of time together, so it is still a process of getting to know each other.”

Romney came out of the dinner praising Trump.

"I have to tell you, I've been impressed with what I've seen in the transition,” Romney said.

"I think you're going to see America continue to lead the world in this century, and what I've seen through these discussions I've had with President-elect Trump, as well as what we've seen in his speech the night of his victory, as well as people he's selected as part of his transition, all of those combined give me increasing hope that President-elect Trump is the very man that can lead us to that better future.”

Trump met with Corker, Giuliani and Romney on Tuesday. He met with Petraeus on Monday.

The transition team said there will be no further announcements pertaining to Cabinet positions this week.

On Wednesday, Trump announced his selections of Steve Mnuchin for Treasury secretary and Wilbur Ross to head the Commerce Department. He has tapped Chicago Cubs co-owner Todd Rickets to act as deputy secretary of Commerce.

Trump has meetings planned in New York City today with former WWE President Linda McMahon, former Georgia Gov. Sonny Perdue, Indiana Sen. Dan Coats Daniel (Dan) Ray CoatsFBI chief says Russia is trying to interfere in election to undermine Biden The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Trump, Biden renew push for Latino support Former Intel chief had 'deep suspicions' that Putin 'had something on Trump': book MORE (R) and retired Gen. John Kelly.

Vice President-elect Mike Pence Michael (Mike) Richard PenceButtigieg stands in as Pence for Harris's debate practice Trump argues full Supreme Court needed to settle potential election disputes Pence adviser knocks ex-staffer who criticized Trump on COVID-19 MORE will be in Washington for meetings with Priebus, Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.), Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Senate GOP aims to confirm Trump court pick by Oct. 29: report Trump argues full Supreme Court needed to settle potential election disputes MORE (R-Ky.), former Secretary of State Condoleezza Rice, Iowa Gov. Terry Branstad and Rep. Jeb Hensarling (R-Texas), the chairman of the House Financial Services Committee.

On Thursday, Trump and Pence will head to Indianapolis to unveil details about their deal with air-conditioning giant Carrier.

In March, Carrier announced it would close its facility in Indianapolis, Indiana and move its operations to Mexico, thereby eliminating 1,400 American jobs.

But Trump and Carrier announced late Tuesday that they’d reached a deal to keep 1,000 manufacturing jobs in Indiana, fulfilling a major promise the president-elect made during the campaign.