San Francisco, California – Mark Zuckerberg has downplayed Elon Musk's suggestions that their rumored cage fight is close to being arranged, and told followers not to believe the X CEO's claims.

The Meta owner said on social media platform Threads that none of Musk’s claimed plans had been agreed on. "Not holding my breath," he wrote.

On Friday, Musk wrote on his social platform X that he had asked Italian Prime Minister Georgia Meloni and her culture minister Gennaro Sangiuliano for an historic site for the battle.

"It will not take place in Rome," Sanguiliano said, adding that he had a "long and friendly conversation" with Musk. There had been speculation that two of the world's richest men would battle it out like ancient warriors at the Colosseum in Rome. Musk wrote on his site that Meloni and Sanguiliano had agreed to "an epic location" but he did not name it.

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But later in the day, Zuckerberg said he would be the one to announce the location.

"If he (Musk) ever agrees to an actual date, you'll hear it from me," Zuckerberg wrote. "Please assume there is no agreement on anything he claims."

The rival tech bosses seemingly agreed to a brawl in June when Musk tweeted that he was "up for a cage fight" with Zuckerberg, who asked him to send a location.

Posting on X on Friday, Musk said: "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.

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"I spoke to the PM of Italy and Minister of Culture. They have agreed on an epic location."

Musk added that the event would "pay respect to the past and present of Italy," and "all proceeds would go to veterans."

Responding to the claims, Zuckerberg said on Threads: "I love this sport and I’ve been ready to fight since the day Elon challenged me."

"I’ll share details on my next fight when I’m ready," Zuck added. "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."

It is unclear how fit Musk is. He said on Friday that he needed surgery for a problem with his right shoulder blade, but predicted the recovery would be quick. Musk said he lifts weights on the side but does not have time for training.

Zuckerberg on the other hand works out with martial arts trainers and is visibly fitter than Musk. Zuckerberg posted a photo on his X competitor app Threads showing him in a training cage in his backyard.

Tensions have been high between the two tech billionaires’ companies after the launch of Threads, a text-based conversation app, by Meta in July.

Twitter sent a cease-and-desist letter to Zuckerberg after the launch, claiming Meta had made "unlawful misappropriation of Twitter’s trade secrets and other intellectual property."