The dinner came as the president-elect got a shot in the arm by a manufacturing company announcing a deal to keep nearly 1,000 jobs in the Rust Belt and as the New York billionaire prepared to switch his attentions from job interviews to a post-election victory tour.
"We will keep our companies and jobs in the US. Thanks Carrier," Trump tweeted late Tuesday, referring to the Indiana-based air conditioning company that announced the deal.
The choice of Jean-Georges, a three-starred Michelin restaurant overlooking Central Park run by celebrity French chef Jean-Georges Vongerichten and popular with New York high society, was the clearest indication yet that Trump may select Romney as his chief diplomat.
After the dinner, Romney offered words of praise for Trump that contrasted sharply with his past criticisms, saying he had been "impressed" by his acceptance speech and subsequent preparations for office, calling it "a wonderful evening."
"I think you're going to see America continue to lead the world in this century," Romney told reporters, saying he had "increasing hope that president-elect Trump is the very man who can lead us to that better future."
The brash real estate tycoon and the former Republican nominee who lost the 2012 election to Barack Obama were joined by Trump's incoming chief of staff Reince Priebus in full view of other diners, who included CNN's senior White House correspondent.
In a restaurant where dinner starts at $148 a head, the Trump team said they feasted on garlic soup with thyme, sauteed frog legs and scallops with caramelized cauliflower and a caper raisin emulsion.
For their main course, both the president-elect and Priebus opted for prime sirloin with a citrus glaze and carrots, and Romney for lamb chops with the mushroom bolognese sauce. All three had chocolate cake.
Asked by a reporter briefly allowed to observe the meal whether it was going well, the president-elect flashed a thumbs up.
- Mnuchin touted -
It was the second face-to-face meeting in 10 days between Trump and the 69-year-old former Massachusetts governor, who savaged him as a "conman" and a "fraud" during the election campaign.
Trump's secretary of state will be America's public face to the world who could face the delicate task of reassuring foreign allies alarmed by the president-elect's rhetoric on the campaign trail.
Other key posts yet to be announced are the secretaries of defense and treasury -- for which US media reported that Trump was expected to name former Goldman Sachs banker Steven Mnuchin.
Romney's distrust of Russia -- at odds with a president-elect who has spoken admiringly of Vladimir Putin -- and the respect he generally commands have been touted as qualities by establishment Americans.
It remains unclear how influential the secretary of state would be on crafting foreign policy with Trump loyalist and retired general Michael Flynn already nominated as national security adviser.
Besides Romney, other potential candidates are celebrated general yet scandal-clad former CIA director David Petraeus, Senate Foreign Relations Committee chairman Bob Corker and former New York mayor Rudy Giuliani.
Earlier Tuesday, Trump met Corker, 64, who said that he thought Trump had narrowed the choice "to a very small group of people" and it was important that he selects somebody on the same wave length.
Petraeus, who met the president-elect on Monday, has by far the most foreign policy experience, but was forced to resign from the CIA after showing classified material to his mistress Paula Broadwell.
In 2015, he pleaded guilty to a misdemeanor charge of mishandling classified materials, and was put on probation and fined $100,000.
- Jobs to stay -
Helping Trump claim success on his election pledge to save American jobs from going overseas, air-conditioning company Carrier Corp announced it had reached a deal with the president-elect and vice president-elect Mike Pence "to keep close to 1,000 jobs."
Trump had tweeted on America's Thanksgiving holiday last week that he was seeking to persuade the company to stay in the United States.
The New York Times reported that Trump and Pence plan to appear at the company's Indianapolis plant on Thursday to announce they have struck a deal after the company had threatened to move 2,000 jobs to Mexico.
The same day, both Trump and Pence are also scheduled to lead a post-election rally in Cincinnati, Ohio.
The evening event at the home of the Cincinnati Cyclones, with a maximum capacity of more than 17,000, is expected to be similar to those that drew enthusiastic crowds of thousands during the campaign.