Boris Johnson jokingly suggested to David Cameron that he should consider becoming Nato's secretary-general during an informal dinner in New York.
The Foreign Secretary met the former Prime Minister at the Red Rooster in Harlem, New York, on Thursday night where the pair set aside past differences.
Several members of the Cabinet are keen for Mr Cameron to take the role at Nato and believe it would enhance Britain's standing after it leaves the European Union.
The former Prime Minister is understood to be one of the front-line candidates for Europe's top defence posting, which comes with a tax-free salary of £222,019.
Sources said that Mr Johnson had only jokingly raised the idea and Mr Cameron had brushed it aside, adding that it is "not remotely" on the cards.
It came as the Foreign Secretary's spokesman denied claims that he and Mr Cameron had been "dad-dancing" during the hour-long meal.
One diner at the restaurant said that he had seen the pair "bopping along", while a Reuters reporter posted a picture of Mr Johnson apparently standing on a chair.
The reporter claimed that a source at the restaurant told her that Mr Johnson was "sloshed" and had "danced a little".
A spokesman for Mr Johnson said it was a "total lie" to claim Mr Johnson had been dancing. He added that he had been trying to get out of his chair when the picture was taken.
The former Prime Minister is understood to have contacted Mr Johnson and asked to join him for dinner after watching him deliver a speech at the United Nations.
During the meal the pair are also understood to have praised Mrs May for her response to the Westminster attacks. "They said she was doing a great job," a source said.
The two men were spotted as they left the restaurant by Joanna Geary, who works for Twitter. She told The Guardian: "As I passed … I instantly recognised the famous mop of hair belonging to Boris Johnson. I said: ‘hello Boris’.”
She said she did not even notice Mr Cameron until the Foreign Secretary said “well then, you’ll recognise my friend David" and pointed to the Prime Minister.
Ms Geary said another diner at the restaurant told her: “Everyone realised they were important, but had no idea who they were… ‘They were just bopping along to the music like the rest of us.”
She said she asked the diner if they were "dad-dancing". "He laughed and said: ‘That’s about the size of it'"
But a spokesman for Johnson said the claim that the foreign secretary was dancing in the restaurant was “a total lie”.
Mr Cameron tried to stay out of politics since stepping down as MP for Witney last September. He charges up to £120,000 for each speech he makes, has become President of Alzheimers Research UK and is also chairing a commission on overseas development.
However earlier this month he was caught on camera in the wake of a backlash over the Government's decision to raise national insurance. "Breaking a manifesto promise, that's stupidity," he appeared to say.