The day after Elon Musk challenged Mark Zuckerberg on social media to “a cage match” last month, Dana White, president of the Ultimate Fighting Championship, received a text.

It was from Zuckerberg, chief executive of Meta. He asked White, who heads the world’s premier mixed martial arts competition, which is fought in cage-like rings, if Musk was serious about a fight.

White called Musk, who runs Tesla, Twitter and SpaceX, and confirmed that he was willing to throw down. White then relayed that to Zuckerberg. In response, Zuckerberg posted on Instagram: “Send Me Location,” a reference to the catchphrase of Khabib Nurmagomedov, one of the U.F.C.’s most decorated athletes.

Since then, White said, he has talked to the tech billionaires separately every night to organise the showdown. On Tuesday, he said, he was “on the phone with those two until 12:45am.” He added, “They both want to do it.”

If you thought that a cage fight between two of the world’s richest men was just a far-fetched social media stunt, think again.

Over the past 10 days, White said he, Musk and Zuckerberg — aided by advisers — have negotiated behind the scenes and are inching toward physical combat. While there are no guarantees a match will happen, the broad contours of an event are taking shape, said White and three people with knowledge of the discussions.

The fight would be an exhibition match, White said, and outside official U.F.C. jurisdiction and rights deals, though he would help produce the event. The tech leaders have agreed there should be a charity component, White and a person familiar with the talks said, with details still being worked out. The preferred location is Las Vegas, which requires approval from the Nevada Athletic Commission. On Thursday, Musk tweeted that the event could also happen in the Roman Colosseum.

Zuckerberg’s friends and advisers have generally supported the match, two people close to him said, though others said a fight would be a distraction and not the best use of his time. One person close to Musk said that while he hated sports and didn’t appear to have the discipline to train regularly, no one could rule anything out with him.

If the matchup between Musk, 52, and Zuckerberg, 39, goes ahead, it would be a rare spectacle, even in the braggadocio-filled universe of the tech industry. While Steve Jobs and Bill Gates used to snipe at each other, the closest the tech world had before this to real sporting feuds was among billionaire yachtsmen like Larry Ellison of Oracle and Hasso Plattner of SAP.

But two wildly wealthy tech titans grappling, punching and kicking in a Las Vegas or Roman arena? No one would have dreamed it. Meta declined to comment. Musk did not respond to a request for comment. Zuckerberg and Musk have long teetered between being competitors, frenemies and outright enemies. The two have criticised each other over the years, including on Musk’s SpaceX rockets, data privacy scandals at Meta and more. Most recently, Zuckerberg dispatched a team at Meta to build a competitor to Musk’s Twitter, code-named Project 92.

“We have two guys that have never professionally fought, and they’re in two completely different weight classes,” White said. Still, he said, “it will be the biggest fight in the history of combat sports.”