The experienced first-five was brought out of the international wilderness to play in the last four matches of the Rugby Championship, helping the Wallabies to two victories over world champions South Africa and two over Argentina.
Under World Rugby regulations, Cooper is eligible for release by his club for the November tests against Scotland, England and Wales, but Australia could not demand his services for Saturday's test against Japan.
New Zealand-born Cooper said that while he "assumed" he would be available to play Japan on Saturday having been involved in training this week, he was uncertain of his status after that.
Wallabies coach Dave Rennie said on Sunday he would not be sticking rigidly to the World Rugby release rules in the spirit of building good relationships with the Japanese clubs, where an increasing number of Australians play.
Rennie also said last weekend that one of Cooper and James O'Connor was likely to start at flyhalf on Saturday, with the other backing up from the bench.