Williams told the Sydney Morning Herald he'd followed Tyson's career from a young age, and said it would be an honour to get in the ring with him.
"I grew up watching Tyson and his fights," said Williams. "It's hard not to admire the power and ferocity of Tyson like so many other sports people around the world.
"It would be a humbling and surreal moment in my life to stare at him and know I was facing one of the greats of the sport. It would be an honour... a career highlight to share the ring with an iconic figure of world sport.
"If it's for a good cause, I'd love to get in the ring with Mike Tyson."
Tyson first sparked chatter about a potential comeback after wowing fans in a ferocious sparring session in a video that went viral, but nothing about returning to the ring has come from the man himself.
Regardless of the return, according to Australian boxing legend Jeff Fenech, Tyson would still put Sonny Bill Williams "in the morgue" if they were to meet in the ring.
Fenech, a good friend and former trainer of Tyson, said the fight is "not going to happen", but if it did, it wouldn't end well for the former footballers.
"Great publicity, but it's not going to happen," Fenech told the Sydney Morning Herald. "They're offering him half a million or a million dollars — he could get more than $20 million to do it in Saudi Arabia. Why would he come here?
"Let me tell you something. If he hits Sonny Bill Williams or Paul Gallen, he will be up for manslaughter.
"I'm serious. If he punched Paul Gallen, he could kill him. These guys have never been punched by somebody like Mike.
"You see what he's doing to the pads, imagine Mike hitting one of those guys with one of those uppercuts. More than likely they will be in the morgue the next day.
"Fighting Sonny Bill? Who has Sonny Bill fought? Sonny Bill won't even fight Paul Gallen because I don't believe he can beat him."
In the initial report, Amatruda claimed he had already begun the process of trying to get Tyson to Australia.
"The first thing I did was contact (celebrity agent) Max Markson and ask him to offer Tyson $1 million," he said. "Max brought him to Australia in 2012. He gets on well with him and his wife but the main thing is that he got him a visa to get into the country back then and that's the key."
Tyson got a visa to visit in Australia in 2012, a week after he was denied one by the New Zealand government, due to being convicted of rape in the US in 1992.
As for Williams, the former All Blacks centre is now with the Toronto Wolfpack in the UK Super League, and was reported to be in talks to return to the ring next year against Hall.
Williams has a 7-0 professional record, but has not fought in a pro bout since 2015, or a charity bout since 2018.