Mr Musk posted a message on his social media platform Twitter that he was "up for a cage fight" with Mr Zuckerberg.

Mr Zuckerberg, the boss of Facebook and Instagram parent company Meta, then posted a screenshot of Mr Musk's tweet with the caption "send me location".

"The story speaks for itself," a Meta spokesperson told the BBC.

Mr Musk then replied to Mr Zuckerberg's response with: "Vegas Octagon."

The Octagon is the competition mat and fenced-in area used for Ultimate Fighting Championship (UFC) bouts. The UFC is based in Las Vegas, Nevada.

Mr Musk, who turns 52 later this month, also tweeted: "I have this great move that I call 'The Walrus', where I just lie on top of my opponent & do nothing."

He later tweeted short videos of walruses, perhaps suggesting his challenge to Mr Zuckerberg may not entirely be serious.

He also tweeted: "I almost never work out, except for picking up my kids & throwing them in the air."

Meanwhile, 39-year-old Mr Zuckerberg has already been training in mixed martial arts (MMA) and has recently won jiu-jitsu tournaments.

Twitter did not provide a statement when contacted by the BBC for comment.

The exchanges have gone viral with social media users debating who would win the bout, while others have posted memes including mocked up posters advertising the fight.

For example, business consultant Seyi Taylor tweeted: "Choose your fighter" with pictures of the two tech bosses.