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David Nucifora, the national high performance unit boss, who was a major player in putting together Cooper's contract, said any suggestions the ARU wanted to ditch the controversial Queensland Reds star were way off the mark.
"If the aim was to get Quade to leave then that's what would have been done," Nucifora said.
"The fact that it's been put out there that it was a rookie offer was not accurate.
"He was given a substantial offer and an offer that if he chooses to accept, he will be well rewarded.
"The fact he's been given an offer means we want to keep him."
Nucifora hasn't heard anything from Cooper or his manager Khoder Nasser.
"We haven't had any contact with them so it's a bit hard to make a comment. We haven't been told officially where things are at from their point of view," he said.
"It's not frustrating, it's just the reality of the way people go about their business at times.
"Until we're contacted and told formally what the situation is, it's pretty hard to have a position on it."
Cooper is considering his future after the ARU reportedly offered him a downgraded, incentive-based contract. If he does not accept an ARU offer the three-year Reds deal he signed in June effectively becomes redundant.
The ARU offer came after a difficult season in which Cooper battled with injury while also being heavily fined for referring to the Wallabies as a "toxic environment".
The 24-year-old is said to be poised to quit Australian rugby to either continue playing overseas, switch to rugby league or possibly even turn to boxing.
Nasser said on Monday Cooper would hold a press conference next week.
Nucifora said there was no deadline from an ARU perspective on when the matter would be resolved.
"You can't force these things, it's up to the other side. It's up to them to respond when they want to bring it to a head. We just have to sit back and wait," he said.