The New Zealand-born 23-year-old missed training on Friday with a bout of flu.
Skipper Rocky Elsom believes that Cooper will be fine in time for the opener at Sydney’s ANZ Stadium.
"If he's not feeling that well, it's probably a good move not to train but I think he'll be fine tomorrow," the captain said at a press conference.
Cooper was replaced in training by full-back Kurtley Beale, but if the illness persists it could mark a return to the squad for the ousted Matt Giteau.
Giteau was dropped from the starting lineup following Australia’s shock defeat to Samoa on Saturday.