Mr Musk, owner of social media platform X, formerly Twitter, earlier appeared to suggest the fight would be held in an “epic location” in Italy.
He outlined streaming options and an ancient setting for the proposed event, claiming he had spoken to Italian Prime Minister Giorgia Meloni.
The rival tech bosses seemingly agreed to a brawl in June when Mr Musk tweeted that he was “up for a cage fight” with Mr Zuckerberg, who asked him to “send me location”.
Posting on X on Friday, Mr 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.
“I spoke to the PM of Italy and Minister of Culture. They have agreed on an epic location.”
Mr 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, Mr Zuckerberg said on Threads: “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.
“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.”
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 Mr Zuckerberg after the launch, claiming Meta had made “unlawful misappropriation of Twitter’s trade secrets and other intellectual property”.
UK former prime minister Boris Johnson weighed in on the potential bout, claiming he would back Mr Musk to win and suggesting it would be “bigger than the Rumble in the Jungle” between Muhammad Ali and George Foreman in 1974.
Writing in his Daily Mail column and referring to an ancient Greek sport, he added: “By the way, if the Musk-Zuckerberg bout does go ahead, I challenge the winner to a Cumberland wrestling pankration. And as prize money I propose that the victor should receive half the other’s annual income.”