Mark Zuckerberg says he is "not holding his breath" over the proposed bout between himself and Elon Musk taking place.
The Facebook founder says he suggested the date of 26 August to his fellow tech entrepreneur, but Musk has not responded.
Posting on his new platform Threads, Zuckerberg also claimed he was "ready today" to enter the ring.
In a gentle jibe at his would-be opponent, Meta's CEO also responded to Musk's claim that the fight would be streamed on X (formerly known as Twitter).
"Shouldn't we use a more reliable platform that can actually raise money for charity?" he quipped.
Zuckerberg continued the Silicon Valley based trash-talk by responding to a follower who asked if the decision to stream on X had been mutually agreed, writing: "More like 'funding secured'."
This is a reference to a claim that Musk made in 2018 about taking Tesla private, which saw him fined $20m (£16m) by US regulators.
Posting on Sunday morning, Musk said that the proceeds of the fight would go to veterans charities.
He also said he is "lifting weights throughout the day, preparing for the fight", adding: "Don't have time to work out, so I just bring them to work."
A video on X showed Musk lifting weights while in his San Francisco office.
Both men have been teasing each other over the fight, which so far has not been formally announced.
Musk described the clash as "a civilised form of war" - adding that "men love war" when asked what the point of the bout was.
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."
"Vegas octagon," Musk responded.
Musk, who completed a $44bn (£35bn) takeover of Twitter last October, joked: "I have this great move that I call 'The Walrus', where I just lie on top of my opponent & do nothing."
He also posted: "I almost never work out, except for picking up my kids & throwing them in the air."
Zuckerberg on the other hand won gold and silver medals in his first jiu-jitsu tournament last month.
Skysports