Cooper has been the subject of criticism in Australia for inconsistent performances but Williams has been quick to defend the talented fly-half.
"If people are saying he is not wanted in rugby... if they think he is not good enough to be playing for Australia then I would love to lure him across to rugby league for a year," Williams told Australia's Sunday Telegraph.
"I will try. I would definitely love to play alongside him. I think he would be a success - I have spoken to him about it."
Williams added: "I don't have to make a case for him, you just have to click on YouTube to see what he is capable of."
Williams is currently with Japan's Panasonic Wild Knights.