Cooper said he wants to swap codes and give the 13-man game "a fair crack" with Williams, a good friend of his, at the Toronto Wolfpack before the pair retire.
"I want to play with Sonny before we both retire. But I wouldn't mind playing NRL either, just for one season or even just come and do some training with the lads to see what it is like," Cooper said on the Ice Project podcast.
"If it doesn't happen, it doesn't happen. I am happy with what I have been able to achieve, but if the opportunity arose I would love to do it."
The 31-year-old is currently playing for the Kinetsu Tigers but admits league has always captured his attention, even since his early playing days in Tokoroa.
"A lot of people say I would come and kill it, and I know I can play it," he said.
"For me it seems easy in terms of the theory... athletically though, it is a lot harder.
"I look at the game and every time I watch it, I know how much I would love to play and test myself at a professional level. I still want to play, it's just figuring out whether it is possible."
Cooper also revealed he was actually close to making the code swap back in 2010 when he almost put pen to paper with an NRL club, but he didn't want to give up on his rugby union dreams.
"I basically signed with Parramatta, and then I dropped my nuts and pulled out," he said.
"I was scared and felt like I would miss out on achieving what I wanted to achieve in rugby. I didn't want to be a guy that floated in between and did nothing.
"I am sort of glad I didn't go to Parra because a year later we won the comp with the Reds, and Parra didn't do too well after that."
Cooper went on to earn 70 Test caps with the Wallabies and played in the 2015 Rugby World Cup final against the All Blacks.