Fly-half Cooper has made himself unavailable to coach Robbie Deans after describing the atmosphere within the national team as "toxic".
The comments, which came on Australian television, prompted O'Neill to release a statement, in which he said the decision to return to the Wallabies rested squarely with Cooper.
"In light of Quade's interview last night, we feel compelled to respond because he has moved beyond his comments of the weekend," O'Neill said.
"He talks of an unhappy environment without elaborating.
"He uses the word 'toxic' - an extremely strong descriptor.
"However, when pressed on the issues he turned to facilities and the Wallabies not having a dedicated place to train.
"We've never had these concerns raised previously.
"The fact is the Wallabies are a national team. They train, stay and play in cities all around the country and overseas.
"The Australian cricket team and the Socceroos, same thing.
"Suggesting the Wallabies are under resourced has equally come out of the blue.
"Most disturbingly, he was firm about not playing for the Wallabies unless things change.
"If that is how he feels, then that is his choice.
"The reality is a decision on whether or not he stays in Australian Rugby has to this point rested with him since he received an ARU offer in early July."