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Cooper's rugby future is in doubt after his employers the ARU offered him only an incentive-based contract usually reserved for rookies. The 24-year-old was Australia's highest paid player last year.
A move to Japan or Europe or a switch to rugby league are on the cards following the snub which came after Cooper described the culture at the Wallabies under coach Robbie Deans as "toxic". He was fined $60,000 and suspended for three matches for the outburst on Twitter in September.
It is understood that Cooper, who is good friends with former All Black Williams and has the same manager, Khoder Nasser, is keen on boxing and could even fight on the undercard of Williams' proposed bout with Francois Botha in February.
A Sydney television station said Cooper had "quit" the ARU but a spokesman from the organisation said: "We've had no communication from Quade or his management regarding his contract over the past few days."
If Cooper has split with the ARU, his new three-year deal with his Reds Super Rugby team is in severe doubt, but Queensland Rugby Union chief executive Jim Carmichael told the Brisbane Courier Mail he still expected the first-five to turn out for his team next year.
"I know the ARU have recently met with him and I'm respectful that they will have mapped out what 2013 looks like for Quade in their eyes as well," Carmichael said.
"I've heard of no issue about him not playing in Australian rugby. I just know there's argy-bargy in every contract negotiation."
Williams, who left the All Blacks this year to play rugby in Japan and has now signed with the Sydney Roosters, was allowed to box during the rugby season as it allowed the New Zealand Rugby Union to pay him less.
He has said he will not fight during the NRL season.
Cooper, who was born in Tokoroa, provoked strong reactions during last year's World Cup in New Zealand after his constant on-field baiting of All Blacks captain Richie McCaw, which included a knee to the head in a match in Brisbane.
Cooper said he was happy to be regarded as New Zealand's Public Enemy No1 but played poorly in the tournament which ended for him in a knee injury.