All Blacks assistant coach Ian Foster said they would prepare this week for either Cooper or Brumbies pivot Matt Toomua to start, while Israel Dagg noted McKenzie could even pick Waratahs No10 Bernard Foley.
McKenzie said a few days ago when he named his squad for the tournament that he wouldn't make an early announcement on his starting first-five.
"We don't need to make a decision publicly about the playmaking role until one hour before the game," he said.
Such mind games don't bother Foster.
"I haven't really thought that far ahead," he said in regards to who might play first-five for Australia. "I mean if they don't want to name it, they don't want to name it.
"We are preparing for Cooper and Toomua so it's not that big an adjustment, to be honest, and our defensive system has to deal with whoever plays and most of the guys have played against both players all year."
Neither Foley nor Toomua, both 23, have played test rugby before but both have guided their respective Super Rugby outfits well this year.
Cooper needs less of an introduction and the enigmatic playmaker has been through his share of ups and downs in his 38-test career, which has been given a lifeline by McKenzie after Cooper fell out with former coach Robbie Deans.
James O'Connor played five-eighth in Australia's 2-1 series loss to the British and Irish Lions in June with little success and, given McKenzie has three other recognised No10s in his squad, it will be interesting to see where the talented O'Connor fits in.
One of the other players who adds to the Wallabies' mysterious ways is outside back Israel Folau, who has played only three tests in his first year of rugby after moving from AFL, having previously excelled in rugby league.
Folau was a dangerous player for the Waratahs in his maiden Super Rugby campaign but it remains to be seen whether he will play on the wing or at fullback under McKenzie.
Foster acknowledged the All Blacks had to be wary of Folau but said they wouldn't pay him special attention.
All Blacks second-five Ma'a Nonu came through training well yesterday as he continued to recover from an ankle ailment. Foster said he is likely to be fit for selection.
The All Blacks will name their match-day 23 for Saturday's test on Thursday.