Former Massachusetts Gov. Mitt Romney is reportedly President-elect Donald Trump's top choice to lead the State Department in his administration, according to The Wall Street Journal.

Romney, the 2012 Republican nominee for president, met with Trump over the weekend. Sources familiar with the transition team's deliberations told the Journal that Trump is leading toward picking him for secretary of state.

But the decision is not yet set in stone — the Journal reported that some in Trump's orbit want him to instead pick former New York City Mayor Rudy Giuliani, who was viewed as the early frontrunner for the post. Others want him to look at other candidates aside from those two.

See photos from their meeting

8 PHOTOS Romney and Trump meeting See Gallery Romney and Trump meeting Former Massachusetts Governor Mitt Romney arrives to meet with U.S. President-elect Donald Trump and Vice President-elect Mike Pence at the main clubhouse at Trump National Golf Club in Bedminster, New Jersey, U.S., November 19, 2016. REUTERS/Mike Segar Former Massachusetts Governor Mitt Romney arrives to meet with U.S. President-elect Donald Trump and Vice President-elect Mike Pence at the main clubhouse at Trump National Golf Club in Bedminster, New Jersey, U.S., November 19, 2016. REUTERS/Mike Segar U.S. President-elect Donald Trump and Vice President-elect Mike Pence (R) greet former Massachusetts Governor Mitt Romney (L) as he arrives for their meeting at the the main clubhouse at Trump National Golf Club in Bedminster, New Jersey, U.S., November 19, 2016. REUTERS/Mike Segar BEDMINSTER TOWNSHIP, NJ - NOVEMBER 19: President-elect Donald Trump (C) and vice president-elect Mike Pence (R) welcome Mitt Romney (L) to the clubhouse at Trump International Golf Club, November 19, 2016 in Bedminster Township, New Jersey. Trump and his transition team are in the process of filling cabinet and other high level positions for the new administration. (Photo by Drew Angerer/Getty Images) US President-elect Donald Trump welcomes Mitt Romney as he arrives for a day of meetings at the clubhouse of Trump National Golf Club November 19, 2016 in Bedminster, New Jersey. / AFP / Don EMMERT (Photo credit should read DON EMMERT/AFP/Getty Images) US President-elect Donald Trump and Vice President-elect Mike Pence welcome Mitt Romney as he arrives for a day of meetings at the clubhouse of Trump National Golf Club November 19, 2016 in Bedminster, New Jersey. / AFP / Don EMMERT (Photo credit should read DON EMMERT/AFP/Getty Images) BEDMINSTER TOWNSHIP, NJ - NOVEMBER 19: President-elect Donald Trump (L) and vice president-elect Mike Pence (R) welcome Mitt Romney (C) to the clubhouse at Trump International Golf Club, November 19, 2016 in Bedminster Township, New Jersey. Trump and his transition team are in the process of filling cabinet and other high level positions for the new administration. (Photo by Drew Angerer/Getty Images) US President-elect Donald Trump (L) and Vice President-elect Mike Pence (R) welcome Mitt Romney as he arrives for a day of meetings at the clubhouse of Trump National Golf Club November 19, 2016 in Bedminster, New Jersey. / AFP / Don EMMERT (Photo credit should read DON EMMERT/AFP/Getty Images) Up Next See Gallery Discover More Like This HIDE CAPTION SHOW CAPTION of SEE ALL BACK TO SLIDE

A top Trump ally, former House Speaker Newt Gingrich, hinted Monday that he viewed Giuliani as the stronger pick.

"I think that entirely is a question of the president-elect and deciding whether in fact Romney would be willing to be his secretary of state or in fact Romney would work to make Trump Romney's version of the presidency," Gingrich said.

He added: "I think, they've got to talk it through. I am for whoever the president-elect picks. I think there are huge advantages to Rudy Giuliani frankly, I think that, if you want someone who is going to go out and be a very tough negotiator for America and represent American interest in the way that Trump campaigned, I think that probably Rudy is a better pick and has the right temperament."

Giuliani was one of Trump's earliest supporters, while Romney became one of Trump's most vocal critics throughout the campaign.

Romney spoke out against Trump frequently and refused to endorse him despite Trump endorsing Romney in 2012. Romney declined to say who he voted for in the general election.

Trump also torched Romney during the campaign, calling him a "spoiled brat" and "nasty guy."

After the election, Romney said on Twitter he wished Trump the best.

Other developments Tuesday indicate Trump's cabinet is starting to shape up. He tweeted on Tuesday that he's "seriously considering" retired neurosurgeon and former Republican presidential candidate Ben Carson for secretary of the Department of Housing and Urban Development.

The Journal also reported that Trump was likely to name retired Marine Gen. James Mattis as secretary of defense and favors Nikki Haley as a leading candidate to be the US ambassador to the United Nations.

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