Earlier in the day, Musk posted on Twitter, saying: "I'm up for a cage match if he [Zuckerberg] is lol."
Zuckerberg posted a screenshot of the tweet on social media, saying: "Send me location" - the response which echoes the famous line uttered by former Russian UFC champion Khabib Nurmagomedov.
Alex Heath, an editor at The Verge, tweeted that a Meta spokesperson confirmed Zuckerberg was serious about fighting Musk. "The story speaks for itself," a spokesperson said, referring to Zuckerberg's post.
Musk replied to Heath's tweet, saying: "Vegas Octagon," in reference to the UFC Octagon in Las Vegas, thus naming the location for the fight.
"I have this great move that I call 'The Walrus,' where I just lie on top of my opponent & do nothing," Musk added on social media.
The feud comes following reports that Meta plans to launch a rival platform to Twitter, dubbed Threads.
*banned in Russia as an extremist organization