Cooper was told last year by new Queensland Reds coach Brad Thorn that he was not in his plans for Super Rugby, not required at training and the side would not stand in his way if he was offered a contract with another team.
The 29-year-old Cooper is contracted with both the Reds and Rugby Australia until 2019 and being paid a reported A$700,000 a season to essentially play low level club rugby in Brisbane.
"I think it's just a waste for Australian rugby," Giteau, who played 103 times for the Wallabies, told Australia's Fox Sports on Thursday.
"I think he brings so much to a team and obviously if the Reds aren't going to use him, then another franchise should still have the opportunity of getting him.
"He should be training with guys even if he's not going to be picked to play. I'm sure there's a lot of advice (he could pass on).
"He's got 70-odd tests, I'm sure this guy has got something that he can help with."
Thorn has used Jono Lance at flyhalf this season with teenager Hamish Stewart his understudy.
The Reds, who won their only Super Rugby title in 2011 but have been in a downward spiral since, have shown early-season signs of resurgence under Thorn.
While they were beaten by the Melbourne Rebels in their opening game, when they had captain Scott Higginbotham sent off inside the first 10 minutes, they have shown some new found resilience to grind out wins against the ACT Brumbies and Bulls.
They face the Jaguares in Buenos Aires on Saturday.
(Writing by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
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