Cooper's wait for a first test appearance this year goes on after he was dropped off an extended nine-man bench for Saturday's (Sunday morning AEDT) match at Cardiff's Millennium Stadium.
Cheika has opted for a 6-2 split of forwards to backs on his bench, with Rob Horne and Will Genia preferred to Cooper as utility options.
Skipper Michael Hooper said the forward-heavy bench, which includes uncapped prop Tetera Faulkner, reflected Australia's intent to overpower a tough Wales pack.
"I think it's about finishing strong," Hooper said on Friday.
"We know that the Welsh have a very good backrow, a very good forward pack, so I think what our bench shows is we've got to finish strong in that area and have a big, physical impact on the game.
"We've got guys there like Will (Skelton), Kev (James Horwill), Hodgo (Matt Hodgson), who gets through a hell of a lot of work, that's what we've signified there."
Cooper started in last weekend's 40-36 win over the Barbarians, while he was an unused substitute in last month's one-point loss to the All Blacks, denying him a first test appearance since returning from shoulder injury.
The 26-year-old's latest omission comes as a setback to his hopes of winning back the No.10 starting spot from incumbent Bernard Foley but there was clearly no-ill feeling between Cooper and Cheika on Friday.
The pair engaged in a light-hearted but intense pitch-side sparing session after the squad trained under the closed roof at Millennium Stadium.
Cheika said on Friday it was a luxury to have the likes of Cooper and Genia fighting to get back in the team as they both worked their way back from lengthy injury layoffs.
"That's what we should be having, players of that quality fight for positions," Cheika said.
"Those lads in particular haven't had a lot of game time.
"Quade Cooper hasn't played much football at all so it's just a matter of getting time under their belts and I'm sure they're going to be pushing for places."
Australia have won nine straight matches against the Welsh but Hooper played down the significance a tenth straight victory would represent ahead of the sides meeting at next year's World Cup.
"It's all about a building phase for us," Hooper said.
