Trump Pence Bedminster

President-elect Donald Trump (left) and Vice President-elect Mike Pence walk to the clubhouse Saturday at Trump National Golf Club in Bedminster.

(Carolyn Kaster | The Associated Press)

BEDMINSTER -- Gov. Chris Christie is scheduled to meet with Donald Trump on Sunday at the president-elect's Somerset County golf course, where Trump and his transition team are huddling this weekend with candidates for key posts in the upcoming administration.

The meeting with Christie comes amid ongoing speculation over whether the governor is set to leave New Jersey for a job in Trump's White House after being demoted recently from his spot as the transition's chairman.

On Saturday, the biggest name on Trump's itinerary was 2012 GOP presidential nominee Mitt Romney, who arrived at Trump National Golf Club in Bedminster just after 1 p.m.

On Sunday, Trump is also slated to meet with former New York City Mayor Rudy Giuliani -- who, like Christie, was a top Trump campaign adviser and is now a vice-chair of the transition team.

It was initially reported that Christie was supposed to be on site Saturday at the club. But the governor is not expected to be here until sometime Sunday, said Stephanie Grisham, a Trump spokesman.

Speculation about Christie's relationship with Trump has been rampant in recent days after the governor was removed as transition team chairman last week and demoted to one of several vice-chairs.

Christie was long thought to be a contender for a top spot in Trump's administration -- possibly as U.S. attorney general or White House chief of staff.

But numerous reports citing anonymous sources have said there has been tension among Christie and Trump's inner circle. On Saturday morning, Politico published a report saying Trump called Christie last week to voice concerns about the ongoing fallout from the Bridgegate scandal and Christie's handling of the transition efforts.

Brian Murray, a spokesman for the governor, did not immediately return a message from NJ Advance Media seeking comment.

Christie said Thursday that he plans to finish out the last year on his second and final term as governor, though he did not rule out possibly accepting a job in the administration.

Trump is slated to meet Saturday with another New Jersey figure: Lew Eisenberg, a Rumson relative who is a top Republican fundraiser in the Garden State and a former Port Authority chairman.

Eisenberg was also the finance chair for a joint fundraising effort between Trump and the Republican National Committee during the 2016 campaign.

Former Massachusetts Gov. Mitt Romney (left) meets with President-elect Donald Trump and Vice President-elect Mike Pennce outside the clubhouse of Trump National Golf Club in Bedminster on Saturday afternoon.

He is reported to be in the running for Trump's secretary of commerce. Christie has also been mentioned as a possible choice for that spot.

Trump and Vice President-elect Mike Pence walked into the course's clubhouse just before noon Saturday.

Both posed for pictures outside before entering the buiding. Asked about his schedule for the day, Trump said: "A lot of meetings, thank you."

Romney, a frequent Trump critic who is now reportedly being considered for secretary of state, arrived in a white SUV about an hour later.

Trump and Pence greeted the former Massachusetts governor at the front door of the clubhouse.

"Mr. President-elect, how are you, sir?" Romney asked as he shook hands with Trump.

"How are you, sir?" Trump replied before the three walked into the clubhouse to meet.

About an hour later, Romney emerged from the building. Trump and Pence walked him outside and waved to the cameras.

"We had a far-reaching conversation with regards to the various theaters in the world where there are interests of the United States of real significance," Romney told reporters.

"We discussed those areas, and exchanged our views on those topics -- a very thorough and in-depth discussion in the time we had," he added. "And I appreciate the chance to speak with the president-elect and I look forward to the coming administration and the things that it's going to be doing."

Romney spoke for about 30 seconds before getting into his vehicle to leave.

Matt Arco may be reached at marco@njadvancemedia.com. Follow him on Twitter @MatthewArco or on Facebook. Follow NJ.com Politics on Facebook.

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