Former Florida governor Jeb Bush and Mitt Romney, shown here in 2012, will meet this week to discuss their potential plans for 2016. (Melina Mara/THE WASHINGTON POST)

Former Florida governor Jeb Bush flew to Utah on Thursday to visit with 2012 nominee Mitt Romney, bringing together two of the Republican Party’s top potential presidential candidates for a private meeting to discuss their plans.

Kristy Campbell, a Bush adviser, said the huddle had been planned for weeks — before Romney surprised many Republicans by declaring interest in trying to run for the White House again in 2016.

“This meeting has been on the books for some time,” Campbell wrote in an e-mail before the meeting with Romney, adding that Bush “respects him very much.”

Aides to both former governors declined to provide details on the substance of their talks.

If Bush and Romney both decide to pursue the 2016 GOP nomination, the two would be in direct competition for establishment support, crowding an already packed field with two well-respected center-right heavyweights.

Could the third time be a charm for Mitt Romney? The former Republican presidential candidate is making moves to explore another possible White House bid, according to sources. The Post's Karen Tumulty explains what's happening behind the scenes, and what it could mean for the 2016 GOP field. (Julie Percha/The Washington Post)

Thursday’s meeting — first reported by the New York Times — comes after weeks of Bush and Romney quietly trying to ascertain each other’s motives and playbook. Bush has met with Romney’s former donors, while Romney met shortly before Christmas with Bush adviser Mike Murphy and inquired about Bush’s preparations, according to political consultants who know both men.

Ryan Williams, a former Romney campaign aide, said the former Massachusetts governor “has always had a tremendous deal of respect for Governor Bush, and I suspect any meeting is simply an opportunity to check in.”

Romney has said little publicly about Bush, but in exchanges with intimates, he has focused on Bush’s past advisory work for Lehman Brothers and Barclays, two major financial institutions. He argued that it makes Bush vulnerable to the same kind of Democratic attacks he faced in 2012 over his career as Bain Capital co-founder and chief executive.

He has also voiced doubts about Bush’s political skills and ability to beat likely Democratic candidate Hillary Rodham Clinton. A new Washington Post-ABC poll released Thursday suggested Clinton holds double-digit leads over both Bush and Romney.

Alex Castellanos, a Republican strategist who has worked for both men, said Romney is finding it difficult to make a compelling argument for a third national campaign, especially among party officials and donors.

“Mitt Romney has had a billion dollars and two attempts to try to tell America why he should be president, and he hasn’t been able to do it,” Castellanos said. “He has been able to tell us why Obama shouldn’t be president, but not why he should. That’s why a fresh new crop of Republican candidates is a mortal threat to him.”

Romney agreed to the meeting in the weeks following the 2014 midterm elections, and has described it in casual terms to friends as a chance to reconnect with one of the GOP’s central players. Bush has described the Romney meeting as one of many he has requested as he moves closer to a campaign, according to Republicans who requested anonymity to discuss private conversations.

Romney ally Mike Leavitt, the former Utah governor, played down the rivalry. “They have been trying to get it scheduled months ago, and it’s zigged and zagged on the schedule until it happened to come together today,” he said in an interview. “This is nothing beyond two people who like each other concluding it would be good to show their friendship is intact as they both start down the road of making an important decision, where they both may be seeking the same objective.”

Of particular interest to Bush is sharing with Romney the details of his “right to rise” slogan, which has become the name of Bush’s affiliated political action committees and the core message of his emerging campaign, according to Republicans familiar with his thinking. Echoing Rep. Paul Ryan (R-Wis.) and the late New York congressman Jack Kemp, Bush has been putting an emphasis in his public remarks on closing the rising gap between the rich and the poor.

Confidants of both men also said that Bush and Romney are trying to get a better sense of where they each stand in the early stages of the race — organizationally, politically and personally, especially in Romney’s case. Bush associates remain unsure of whether Romney is seriously preparing to enter the contest.

Bush flew alone to Salt Lake City on a commercial airliner from Reagan National Airport on Thursday morning. Before boarding a Delta Air Lines plane at the gate in Northern Virginia, he was spotted by reporters who asked him about Romney. “I like to ski. I can’t comment,” Bush told a CBS News correspondent. (A Bush adviser later clarified that Bush was joking about skiing with Romney.)

Once Bush landed in Salt Lake City, he was confronted by a large group of local television and print reporters. When he walked toward a waiting black SUV, some fans asked him to sign baseballs.

“It’s still early, it’s January,” Bush told reporters. One man came up to Bush during the scrum and said, “Thank you, Mr. President!”

A reporter from KUTV, a CBS-affiliated television station, asked Bush whether the session with Romney would be uncomfortable. “Nah, not at all,” Bush said. “I respect him a lot. I admire him a lot. He is a great American. I look forward to seeing him.” Asked about the topic of their discussion, Bush said, “the future.”

Philip Rucker contributed to this report.