On Sunday morning, Trump tweeted, "Numerous patriots will be coming to Bedminster today as I continue to fill out the various positions necessary to MAKE AMERICA GREAT AGAIN!"
On Saturday, Romney arrived for his meeting with Trump and members of his transition team at the Trump National Golf Club about 1 p.m. and left shortly before 2:30 p.m.
As he and Trump emerged from the meeting, the president-elect did not approach the press, but, responding to shouted questions, told reporters the meeting "went great."
But a readout released by the transition team late Saturday said Trump and Romney "had a substantive and in-depth conversation about world affairs, national security and the future of America. It was an extremely positive and productive conversation."
Romney made a brief statement to the media, saying the meeting focused on foreign affairs. He said he "looks forward" to a Trump administration, but would not comment on whether he wants to be a part of it.
"We had a far-reaching conversation with regard to the various theaters in the world where there are interests of the United States of real significance. We discussed those areas and exchanged our views on those topics,” Romney said.
Romney did not respond to shouted questions regarding potential cabinet positions and would not answer questions regarding his previous statements calling Trump a "con man" and a "fraud."
Sources on Trump’s transition team told ABC News on Thursday that Romney, the 2012 Republican presidential nominee, is under consideration for secretary of state. One senior-level source directly involved in the transition efforts said that Saturday’s meeting is also about “mending fences,” as Trump and Romney have had a contentious relationship.
Trump also met with well-known education activist Michelle Rhee and her husband, Kevin Johnson, mayor of Sacramento; Betsy DeVos, another education activist; and with retired Marine Corps Gen. James Mattis.
After the meeting with Mattis, who is viewed as a possible contender to be nominated for defense secretary, Trump said, "He is the real deal, a brilliant wonderful man, what a career. We'll see what happens. He is the real deal."
And according to the readout, Trump and Mattis "had an incredibly in-depth conversation on plans for national security. The discussion included ISIS, the Middle East, North Korea, China, NATO and other hotspots around the world."
Rhee is a possible contender for nomination as education secretary. The transition team's readout said she and Trump "enjoyed an in-depth discussion about the future of public education in our country. This included the possibility for increasing competition through charter and choice schools. They also brought the idea of merit pay for teachers going above and beyond in their classrooms into the conversation."
As for DeVos, the readout said the conversation was "focused on the Common Core mission, and setting higher national standards and promoting the growth of school choice across the nation."
Of the meeting with Ricketts, the readout said the conversation "involved domestic commerce, ingenuity and growth for our country. Discussions on tax reform regulations and entrepreneurial initiatives were also included."
Trump and Pence "had a great discussion with Mr. Bob Woodson regarding community-based developments and opportunity," the readout stated. "They also discussed plans to strengthen neighborhoods across America and faith-based initiatives."
Regarding Puzder, the meeting focused on "regulations, labor reforms, and freeing up small business loans for new and innovative business ventures," according to the readout. "Discussion on international trade was also included."
In the meeting with Eisenberg, Trump and Pence "discussed plans for America First initiatives, bringing Made in America manufacturing to the forefront and improving infrastructure," said the readout.
Dr. Soon-Shiong joined Trump and Pence for dinner, during which they "discussed innovation in the area of medicine and national medical priorities that need to be addressed in our country," according to the readout.
Trump is meeting with people under consideration for cabinet posts and individuals from whom the president-elect is simply seeking advice and counsel, transition officials said.
Transition officials had previously said an announcement regarding a national security appointment would possibly be made Saturday, but that did not occur. Following the meetings, however, Trump said he may have transition-related news to share on Sunday: "We'll hear some things tomorrow," he told reporters.
When Trump and Pence arrived at the golf club at around 11 a.m., a reporter shouted a question asking if the president-elect was looking forward to the meetings today.
Both Trump and Pence answered in the positive. It was the first question from the press that Trump has answered since his interview on CBS News' "60 Minutes" on Nov. 10, two days after the election.
Trump’s meetings are expected to continue Sunday with New Jersey Gov. Chris Christie, former New York City Mayor Rudy Giuliani and Kansas Secretary of State Kris Kobach, among others, transition officials said.
Kobach, one of the president-elect’s advisers on immigration, is known as an immigration hardliner. He told Reuters recently that Trump's policy advisers had discussed drafting a proposal for the president-elect’s consideration that would reinstate a national registry for visitors and immigrants from Muslim countries. Kobach also said in the interview that Trump's immigration team has discussed drafting executive orders "so that Trump and the Department of Homeland Security hit the ground running."
But on Friday, the spokesman for the transition team on Friday emphasized that Trump is not advocating any kind of broader registry for Muslims.
“President-elect Trump has never advocated for any registry or system that tracks individuals based on their religion, and to imply otherwise is completely false. The national registry of foreign visitors from countries with high terrorism activity that was in place during the Bush and Obama Administrations gave intelligence and law enforcement communities additional tools to keep our country safe, but the president-elect plans on releasing his own vetting policies after he is sworn in,” said Jason Miller, the transition team's communications director.
ABC News’ John Santucci and Veronica Stracqualursi contributed to this report.