Tyson, 53, had been offered $3 million to fight Williams but the Daily Mail says Tyson was unimpressed when promoters floated the idea, saying if he got back into the ring it would be with a real boxer not a rugby player.
Tyson's management had been negotiating with Australian promoters to take part in a multi-million dollar charity bout in Melbourne next year.
Williams, who has had seven fights as a professional for seven wins has said he was willing to get into the ring with Tyson despite his limited boxing experience.
"If its for a good cause, Id love to get in the ring with Mike Tyson", Williams said at the weekend.
"It would be an honour ... a career highlight to share the ring with an iconic figure of world sport.
"I grew up watching Tyson and his fights. Its 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."
The former All Black, now back playing rugby league for with the Toronto Wolfpack, has boxing wins over South African Frans Botha, and American journeymen Clarence Tillman and Chauncey Welliver.
Former Australian world champion Jeff Fenech has expressed concern for Williams should he get in the ring with Tyson saying it would dangerous for Williams given the difference in professional experience between the two.
Tyson revealed recently on social media that he had been training for the past few weeks to get in shape for exhibition and charity matches.
A five-second video clip of him training was posted and immediately impressed boxing afficianados.
Former world champion Evander Holyfield could also loom as a fight for Tyson.
Holyfield claimed wins over Tyson in 1996 and 1997. In the second fight Tyson bit Holyfied's ear, leading to his disqualification.
Holyfield retired professionally in 2001 and Tyson in 2005.