In a series of posts on X, formerly known as Twitter, Musk - the company's controversial owner - said he has been in contact with the Italian prime minister and minister of culture about hosting the event.

But Zuckerberg took to Meta social media platform Threads to say he is "not holding his breath" for Musk to agree to a date.

He said: "I love this sport and I've been ready to fight since the day Elon challenged me.

"If he ever agrees on an actual date, you'll hear it from me. Until then, please assume anything he says has not been agreed on."

He continued: "Not holding my breath for Elon, but I'll share details on my next fight when I'm ready.

"When I compete I want to do it in a way that puts a spotlight on the elite athletes at the top of the game.

"You do that by working with professional orgs like the UFC or ONE to pull this off well and create a great card."

He also posted a picture of himself fighting in his backyard octagon.

He also reconfirmed the fight will be live-streamed on X and Meta.

Musk, 52, wrote: "The fight will be managed by my and Zuck's foundations (not UFC). Livestream will be on this platform and Meta.

"Everything in camera frame will be ancient Rome, so nothing modern at all.

He added: "Everything done will pay respect to the past and present of Italy. And all proceeds go to veterans."

Musk also posted the word "gladiator" with two emojis of swords crossed as well as the Latin phrase Dulce est Desipere in Loco - translated as it is pleasant to be frivolous at the appropriate time.

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This led some X users to speculate that the cage fight may be held at the Colosseum - the largest standing amphitheatre in the world where gladiatorial contests were held during the Roman Empire.

Musk had also previously posted: "Some chance fight happens in the Colosseum."

A spokesperson for the Italian government did not respond to Sky News's questions this afternoon but its culture minister said on Twitter that the fight would not take place in Rome.

The latest development comes after weeks of teasing between the two men over the fight, which so far has not been formally organised.

They agreed to fight in June, when the billionaire Tesla boss wrote he was "up for a cage fight" with Zuckerberg, who replied: "Send me location."

Musk, who bought Twitter for $44bn (£35bn) last October, has said he "almost never works out".

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Zuckerberg, 39, holds a blue belt in jiu-jitsu and recently won gold and silver medals in a tournament. He took up the sport, as well as MMA, during the pandemic and says he now trains three to four times a week.

The animosity between the pair appears to have been sparked by Meta releasing a direct rival to X called Threads, which saw rapid growth on its launch.

Musk threatened to sue Zuckerberg's Meta, claiming he copied X.