The Queensland Reds playmaker, currently sidelined with a knee injury, attacked the ARU and the Wallabies set-up in a series of Twitter posts last weekend.
Cooper (24) said he didn't want to be involved in a toxic environment, raising speculation that he might quit the rugby union and possibly switch to Australia's National Rugby.
The ARU made their first official response to Cooper's comments in issuing a brief statement on Thursday, without elaborating on whether Cooper would be facing any disciplinary action.
"Australian Rugby Union has written to Quade Cooper in relation to social media comments," it said.
"ARU has no intention of conducting those discussions with Quade in the public arena.
"To that end, we will be making no further comment at this stage."
Cooper was critical of Australia's conservative playing style under coach Robbie Deans, warning the Wallabies would continue to lose fans and Bledisloe Tests against New Zealand with conservative tactics.
Cooper said he was only allowed to play his maverick attacking game in Super Rugby for Queensland.
"I love rugby but there's s–t going on behind and above the players [that affects] the whole organisation!" Cooper said in one of his tweets.
When a Twitter follower told Cooper he should be allowed to play in his trademark exciting manner, the Queensland Reds flyhalf responded with an apparent shot at Deans' conservative tactics.
"I am allowed from February to May sir," Cooper said, in reference to his Super Rugby season under Reds coach Ewen McKenzie.
"If people want to go out there and play a boring brand of football then there's other guys they can pick to do that."
'Afraid to say what they feel'
But Cooper later said the tweets were not solely an attack on Deans but on the whole Wallabies/ARU set-up – players, selectors, officials and coaches – which he claimed was not as professional as the last year's Super Rugby champions Queensland Reds.
"There's a lot of people who are afraid to say what they feel so they just go along with it and nothing is going to change," Cooper told Australian Associated Press last weekend.
"That's why I feel so strongly as a player. I don't want to be involved in the toxic environment, and that's how it is at the moment."
Reds chief Jim Carmichael on Wednesday described as "nonsense" speculation of Cooper defecting to rugby league.
Carmichael said while Cooper was "disillusioned at the moment," he had met with the maverick fly-half who confirmed he was "100% committed" to seeing out his three-year Reds contract. – Sapa-AFP