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

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

Mr. White called Mr. Musk, who runs Tesla, Twitter and SpaceX, and confirmed that he was willing to throw down. Mr. White then relayed that to Mr. Zuckerberg. In response, Mr. 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, Mr. White said, he has talked to the tech billionaires separately every night to organize the showdown. On Tuesday, he said, he was “on the phone with those two until 12:45 in the morning.” 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, Mr. White said he, Mr. Musk and Mr. 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 Mr. White and three people with knowledge of the discussions.

The fight would be an exhibition match, Mr. 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, Mr. 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, Mr. Musk tweeted that the event could also happen in the Roman Colosseum.

Mr. 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 Mr. 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 Mr. Musk, 52, and Mr. 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. Mr. Musk did not respond to a request for comment.

Mr. Zuckerberg and Mr. Musk have long teetered between being competitors, frenemies and outright enemies. The two have criticized each other over the years, including about Mr. Musk’s SpaceX rockets, data privacy scandals at Meta and more. Most recently, Mr. Zuckerberg dispatched a team at Meta to build a competitor to Mr. Musk’s Twitter, code-named Project 92.

If they take their rivalry beyond those jibes, the U.F.C.’s Mr. White said he had concerns about the physical gaps between the billionaires. Apart from their 13-year age difference, Mr. Musk is said to be at least 70 pounds heavier than Mr. Zuckerberg. In official mixed martial arts bouts, athletes are generally matched up by weight.

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

Mr. Zuckerberg is especially familiar with the U.F.C. world. Over the past 18 months, he has embarked on a personal journey to bulk up and dove deep into Brazilian jujitsu, a grappling martial art in which competitors try to submit their opponent and which is used in U.F.C. fighting.

Mr. Zuckerberg started training on a lark mostly in his garage in 2021, where he built what he called a “mini academy” with a circle of friends who spar with him. He has said he appreciated that Brazilian jujitsu required “100 percent focus” and strategic thinking to defeat an opponent, rather than brute strength.

Mr. Zuckerberg has sought out martial arts experts, including Dave Camarillo, James Terry and Khai Wu. In May, he competed in his first public martial arts tournament in Redwood City, Calif., which he attended undercover — up until the moment he took off his hat and sunglasses to fight. He won gold and silver medals in the challenge.

Last year, Meta also announced it had partnered with the U.F.C. to bring mixed martial arts fights to Horizon Worlds, its virtual reality app.

Mr. White said Mr. Zuckerberg was truly dedicated to the sport.

“I’ve been talking to Zuckerberg now for maybe close to two years now,” he said. “And there’s never like banter or we’re joking and laughing.” He said the Meta chief executive was “dead serious all the time.”

Mr. Zuckerberg is likely in fighting shape. He has been on a strict workout regimen, going for runs and challenging friends and colleagues to beat his times, two people close to him said. This month, he posted a personal record for completing the “Murph” challenge, which requires completing a series of pull-ups, push-ups, running multiple miles and doing hundreds of squats, all while wearing weighted, military-grade body armor.

“Doing sports that basically require your full attention, I think, is really important to my mental health and the way to stay focused on everything I’m doing,” he said in a recent podcast episode.

Mr. Musk, on the other hand, has tweeted that he “almost never” works out and once suffered a back injury that required surgery after participating in an exhibition with a sumo wrestler. This month, he said he had trained in “judo, Kyokushin (full contact)” — two Japanese martial arts — and “no rules streetfighting.”

“He made that very clear: ‘I’m not going to lose any weight,’” Mr. White said of Mr. Musk’s approach to the potential matchup. “‘Are we going to fight or are we not going to fight?’” Mr. White said Mr. Musk told him.

This week, Lex Fridman, a podcaster, posted photos of himself training judo with Mr. Musk. Mr. Fridman, who has also trained jujitsu with Mr. Zuckerberg, did not respond to a request for comment.

At least one person does not appear to be a fan of a fight: Maye Musk, Mr. Musk’s mother.

“Don’t encourage this match!” she recently tweeted, along with two frowning emojis.