Cooper was seen as the biggest thing in Aussie rugby just over a year ago but a poor World Cup and a nasty ACL injury have seen his stock fall dramatically.
The 24-year-old started the Wallabies' humiliating 22-0 defeat to Williams and his fellow Kiwis a week ago and received even more criticism for failing to spark his side into life as they were kept scoreless for the first time since the early 1970s.
And with Cooper having been previously linked with a move across codes to Paramatta Eels before signing a three-year contract extension with the Australian Rugby Union just three months ago, Williams is keen to play alongside the maverick 10 at in 2013.
"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 the Sunday Telegraph in Sydney.
"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.
"I don't have to make a case for him, you just have to click on YouTube to see what he is capable of.
"(Cooper's skill set is) definitely right up there at the top...in terms of running, offloads, kicking.
"He is such a great talent that he cops a lot of stick, especially in New Zealand. A lot of people have a go at him, but I think that's because he is their biggest threat. It is more of a compliment than anything."