Mr Musk first proposed a fight earlier this month, writing on Twitter that he was “up for a cage match” after rumours emerged that the Meta boss was working on a Twitter rival.
Mr Zuckerberg responded with a screenshot of Mr Musk’s tweet with the caption “send me location”.
A spokesperson for Meta confirmed to The Verge that Mr Zuckerberg’s response was not a joke, saying “the story speaks for itself”.
Mr Musk named a location on Thursday, replying on Twitter to news of the matchup with the words “Vegas Octagon”, referring to the UFC Apex centre in Nevada.
Mr Zuckerberg has previously posted about his martial arts training on Facebook, while also talking extensively about it on podcast appearances.
In May, he competed in his first jiu-jitsu tournament, having trained with UFC prospects in the build-up.
“Competed in my first jiu jitsu tournament and won some medals for the Guerrilla Jiu Jitsu team,” the 38-year-old wrote on Instagram, alongside some photos of him competing and gold and silver medal emoji.
By contrast, the 51-year-old Tesla chief executive claims to not do exercise, writing in a Twitter post on Wednesday: “I almost never work out, except for picking up my kids and throwing them in the air.”
The tech billionaire, who is currently listed as the world’s richest person on the Bloomberg Billionaires Index, hinted in a recent podcast that he would aim to use his superior weight to defeat Mr Zuckerberg.
“I have a move called ‘The Walrus’, which I used on a friend of mine who’s very agile,” he told the Full Send podcast.
“But I was like, let me explain to you why there are weight classes in MMA. I’m going to use a move called ‘The Walrus’, where I just lie on you and you can’t get away.
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