While keeping Folau at fullback would allow the Wallabies to reunite the World Cup centre pairing of Giteau and Tevita Kuridrani, accommodating Adam Ashley-Cooper on one wing means Cheika would have to also relegate either Haylett-Petty or newly appointed vice-captain Rob Horne.
Cheika will name his match-day 23 on Thursday and admits the return of Giteau, Ashley-Cooper, Drew Mitchell and halfback Will Genia from France for Rugby Championship duties has made selection time difficult.
"There's four backs straight back in that are competing for spots and then you've got guys like Lopeti Timani who's really impressed," he said.
"Adam Coleman, now that he's had a bit of experience in June, Dane Haylett-Petty obviously had a really good series in June. (Samu) Kerevi.
"So some of those young guys we blooded in June are competing for spots again and that's a bit of our strategy: bring the guys back in who have got the experience, (get) push from the youth that want to break into the team and squeeze everyone in the middle.
"There's still plenty of time to go on that strategy, but it's starting to happen."
Cheika said he'd have no hesitation breaking up the NSW halves duo of Nick Phipps and Foley, who helped pilot Australia to a 27-19 victory over New Zealand in Bledisloe Cup I in Sydney last year, to pair either with Cooper or Genia.
But he is keeping his cards close to his chest.
(Cooper's) definitely got X-factor, there's no doubt about that," Cheika said.
"There's areas of his game he's really been working hard to improve on and (we're) really, really pleased with him since he's returned into training.
"(He has a) really good work ethic and understands where he wants to improve. He's giving us that in training. We need to be able to turn that into match action."
Possible Wallabies side: Israel Folau, Adam Ashley-Cooper, Tevita Kuridrani, Matt Giteau, Rob Horne, Bernard Foley, Nick Phipps, David Pocock, Michael Hooper, Scott Fardy, Kane Douglas, Rob Simmons, Sekope Kepu, Stephen Moore (capt), James Slipper. Res: Tatafu Polota-Nau, Scott Sio, Tom Robertson, Will Skelton, Sean McMahon, Will Genia, Quade Cooper, Dane Haylett-Petty.
- AAP