Cooper has not played a Test match since last October when the Wallabies played Uruguay in the World Cup, and has not played any rugby since April, for French club Toulon.
The Wallabies have not won a game in New Zealand since 2001, while the All Blacks are undefeated at home against all opposition since 2009, a run of more than 40 Tests.
Cooper, who is New Zealand-born and has always copped plenty from Kiwi crowds, will once again be thrust into the hot seat as he has done several times in his career.
Last year, Cheika left him out of the Sydney Bledisloe, which Australia won, but started him in Auckland where they were hammered and Cooper again copped backlash.
After that match, All Blacks coach Steve Hansen said Cooper is a good player but does not seem to perform in New Zealand.
It's understood the Wallabies will field a new-look starting backline that includes Samu Kerevi in place of Tevita Kuridrani at outside centre, leaving open the option of playing Cooper at inside centre to complement five-eighth Bernard Foley.
Cheika also indicated that Melbourne's rising star Reece Hodge would get his Test debut this weekend, though that is more likely to be off the bench.
"Quade's obviously been there or thereabouts in training, Reece Hodge has also put his hand up quite well at training over the last few weeks," Cheika said.
"It would be a big call for him, but he just looks like he's a lad who's up to it.
"I think we go right back to the very start about attitude and who wants to make it right, and we'll go with the selections from there."
After suffering a record 42-8 loss on home soil last Saturday, the Wallabies have numerous issues to worry about including their general kicking, lineouts, defence and ball retention, but Wallabies backrower David Pocock says the side will only have time to focus on a couple of those.
"You've got to target the areas you think you're going to get the most pay, and we're under no illusions, the All Blacks haven't been beaten over there for a very long time, it's a huge challenge and we're going to have to prepare really well," Pocock said.
"Professional sport, it's about that mental preparation, and that last however many per cent, it's something we'll be working on.
"You look at the way they were able to turn over the ball and capitalise, they've got the players to be able to do that.
"I don't think we built enough pressure.
"There's a huge number of things where we fell well short, and there's no easy way around that.
"We're looking at that this week and trying to change a few things, and prepare with those things in mind for the weekend."
