"You'll hear some things tomorrow," the 70-year-old Republican billionaire president-in-waiting told reporters after a marathon day of meetings at his golf retreat in New Jersey, a 90-minute drive outside Manhattan.
Trump is building his new administration after his shock November 8 election win over Democrat Hillary Clinton, with an eye on his inauguration on January 20.
Romney, the failed Republican presidential candidate in 2012, is reportedly in the running to be Trump's secretary of state, even though the two men traded harsh barbs throughout the White House campaign.
Other high-level candidates who trekked out to Trump's golf resort included retired general James Mattis, a potential Pentagon chief, and Michelle Rhee, the controversial former head of schools in the US capital.
Trump -- with Vice President-elect Mike Pence at his side -- said his meetings had gone "really efficiently. Tremendous talent. We're seeing tremendous talent."
This included talks with Romney, who emerged from the session saying nothing about whether he was offered the job or was interested in it.
"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 said.
"We discussed those areas and exchanged our views on those topics."
Earlier, as Romney walked toward reporters, Trump cupped his hands around his mouth and said, "It went great."
Full schedule
The huge, exclusive Trump National Golf Club Bedminster is one of the president-elect's favorite sanctuaries, where he likes to spend weekends and where he prepared for campaign debates against Clinton.
In addition to Romney, Mattis and Rhee, Trump saw several business leaders including Lew Eisenberg, Andrew Puzder, Betsy DeVos and Todd Ricketts, the owner of the Chicago Cubs baseball team.
Trump called Mattis a "great guy" but didn't say much about his other guests. When asked if the cabinet was being formed Saturday, he replied: "Yes. Partially. We're doing this again tomorrow."
Romney appears to be on the shortlist for the State Department, along with former New York mayor Rudy Giuliani.
Romney would bring a more orthodox Republican worldview to foreign policy. He described Russia in 2012 as the main American geopolitical threat -- a sharp contrast to Trump, who has exchanged compliments with Russian President Vladimir Putin.
During Trump's campaign, Romney described him as a "fraud," rebuking the tycoon for proposals such as banning the entry of all foreign Muslims.
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'Apologize!'
Trump, who was spending his first weekend outside Manhattan since his election, had not appeared in public since he gave reporters the slip to take his family to dinner in New York on Tuesday.
He has however been active on Twitter, where he has won fans -- and detractors -- with his off-the-cuff message style.
Trump unleashed his anger after Pence was booed Friday at a performance of award-winning Broadway musical "Hamilton," and a cast member read a statement urging the new administration to "uphold our American values and work on behalf of all of us."
"Our wonderful future V.P. Mike Pence was harassed last night at the theater by the cast of Hamilton, cameras blazing," Trump wrote Saturday. "This should not happen!"
"The Theater must always be a safe and special place," he added in another message. "The cast of Hamilton was very rude last night to a very good man, Mike Pence. Apologize!"
Trump also tweeted that he had settled three class action lawsuits over his now-defunct Trump University for $25 million so that all his energy could be focused on his new job, dismissing any hint of guilt.
"I settled the Trump University lawsuit for a small fraction of the potential award because as President I have to focus on our country," he tweeted.
"The ONLY bad thing about winning the Presidency is that I did not have the time to go through a long but winning trial on Trump U. Too bad!"
Cabinet takes shape
So far, Trump has announced a handful of government nominations including ultra-conservative Senator Jeff Sessions as attorney general, hawkish congressman Mike Pompeo as CIA director and retired lieutenant general Michael Flynn as his national security advisor.
Flynn's appointment does not require Senate approval.
But that of Sessions as attorney general does, and he has baggage: racially charged comments he made in the 1980s that cost him a chance for a job for life as a federal judge.
With some 15 senior positions in his cabinet still to fill, the property mogul will remain in Bedminster until Sunday night, far from the protesters besieging his New York building.
More than 1,000 demonstrators marched from Queens -- the New York borough where Trump was born -- to Trump Tower in midtown Manhattan on Saturday, decrying what they see as a threat to democratic values under a Trump administration.
Demonstrators, many waving rainbow flags in support of the gay community, carried signs that read: "Queens will resist hatred," "No to fascism" and "Stop racism."
