But with six players to be added on June 11, Cooper will have the opportunity to showcase his skills when Queensland Reds face the Lions on Saturday.
Reds coach Ewen McKenzie appears resigned to Cooper missing out but he insists there is no better player to unlock the Lions' defence.
"I don't think anyone gets picked on one game,'' said McKenzie.
"Quade has played every minute of every (Reds) game so I don't think he can actually do much more.'
"They've picked a squad, he's not in it at the moment. Whether he gets back in or not, that's someone else's call.
"But Quade plays the game because he loves it. He will get out there and do his best.
"You are not going to beat them (the Lions) playing an orthodox game. And someone like Quade, you can't get a better player to do that."
Cooper endured a mixed evening in the Reds' 33-20 victory over Melbourne Rebels on the weekend.
The fly-half saw two kicks charged down for tries but he responded with the boot and clinched a vital try to put the result
Now he is hoping Cooper can play an integral role in a Reds ambush of Warren Gatland's men.
"We are kind of hoping that by the time they get here they will be so busy organising themselves they won't pay too much attention to us and we might be able to do some good things on Saturday,'' added McKenzie.