Branson, founder of the Virgin Group and a supporter of Hillary Clinton's failed presidential campaign, alleged that Trump spent the meeting talking about how to destroy people who refused to lend him money when one of his companies went bankrupt.
In a "Squawk Box" interview, Branson provided this account:
"He invited me to lunch or dinner at his house, and he had just been bankrupt," Branson claimed, later clarifying he meant one of Trump's companies had filed for bankruptcy.
"I thought we would have an interesting conversation about a whole range of issues, and he just spent the whole lunch talking about five people he rung up to try to get help from ... and how these people had refused to help him and how his life's mission was to going to be to destroy these people," Branson asserted.
The White House did not immediately respond to CNBC's emailed request for comment on Branson's claims about meeting Trump and what transpired.
Branson did not provide the exact date of the meeting or identify the Trump company that he said went bankrupt.
It's well-documented that in the 1990s Trump's real estate empire was on verge of collapse. During one of the presidential debates last year against Clinton, Trump referred to steps taken during that time to turn around his company.
Trump, on stage with Clinton, said, "On occasion, four times, we used certain [bankruptcy] laws that are there."
Further defending using bankruptcy in business, Trump said at the time, "I take advantage of the laws of the nation because I'm running a company."
During the campaign, Branson was not shy in criticizing Trump, calling the future president "irrational, aggressive" and lacking informed ideas.