Paul fights at cruiserweight while Williams is a heavyweight.
25-year-old Paul has more than 20 million YouTube subscribers and began a boxing career in an amateur bout four years ago. He has since recorded five victories including two against former UFC Welterweight Champion Tyron Woodley.
Before Williams' victory last week, Lee declared the former NRL premiership winner and Rugby World Cup champion could be turned into a world heavyweight title contender.
Williams has now dedicated himself to boxing after his football career ended and went on a six-week training camp where he sparred with the likes of world champ Tyson Fury, former WBO heavyweight champ Joseph Parker and European champion Tommy McCarthy.
"It's been a pleasure to train Sonny," Lee said during the pair's press conference. "For a man who's achieved so much in the sport world, he's very, very hungry, very, very dedicated, almost obsessive about boxing, so it's been a pleasure to train him.
"If I showed him something this morning, by the next time we met in the gym, I could see that he worked on it, practised it and thought about it, and was already improved at doing it. That taught me all I needed to know about Sonny and how serious he is about the game.
"You might think it's crazy but my ambition for Sonny over the next few years is to build him into a world title contender and eventually fight for the world championship because that's how good he can be. He has that natural ability but you combine that with the hunger he has, I think he can go all the way."
Lee also told the Sydney Morning Herald and The Age: "Is that the greatest story in sports history if he fights for the heavyweight title?"
