Utility back James O'Connor trained at fly-half while Cooper, who recently guided the Reds to the Super 15 title, was confined to his hotel.
But the Wallabies remain confident that the mercurial play-maker will return in time for the clash between the Lions last and next opponents.
"I think he'll be all right," said Australia captain Rocky Elsom.
"It was probably a good move not to train but I think he'll be fine tomorrow.
"It was all right not having him at training, you've got to be able to deal with that and if he's not feeling that well then it's best he just gets better and feels better tomorrow."
Meanwhile, Elsom says he has no concerns over the state of the ANZ Stadium pitch after around 200mm of rain fell on Sydney over the past three days.
"The game might be a little bit slower but I think if it was really badly cut up and really dry that would be more of a concern," added Elsom.
"We've got a game plan that we think can adapt to both wet and dry conditions.
"Obviously if it was like it is now it's not going to be as free flowing, but that's not necessarily a problem."
But Elsom, who enjoyed lifted the Heineken Cup with Leinster in 2009, emphasised the importance of discipline in the wet conditions give the presence of Morne Steyn in the Springboks starting XV.
"When you get into a game that's potentially a little bogged down points become more valuable, and with a bloke like him on the pitch your discipline's got to be right up there.
"We've spoken about that as a group but I guess the proof will be in the performance tomorrow.
"We've got an idea how we think they might play ... but they do a pretty good job at what they do nearly all the time so we've seen a fair bit of that in the past."
"They're physical and it's a physical game but I guess every team is physical.
"It's about who's the most dominant on the night that counts, and if they're more physical than us or they win that battle, then they'll go a long way towards winning the match and vice versa."