VIDEO: Australia eye England
VIDEO: Australia eye EnglandSHARE
The clash at Twickenham will see two Aussie coaches going head-to-head, but Cheika said any talk of rivalry between him and former clubmate Eddie Jones was "irrelevant".
"It is Australia versus England, that's all that counts. It is not about having any fun with Eddie, we will have fun on our own in our own camp and then we will prepare ourselves each day the best we can," said Cheika in the wake of his side's 29-21 victory, their 13th in a row against Wales.
"We understand that the pundits over here don't think we have much of a chance and they have already given England 3-0 for November.
"One guy said: 'All respect to Australia, but a decent club side would beat them'. So I don't think there is too much for them to worry about. We will prepare every day like we are going to play our best game on Saturday and go from there."
The Wallabies were forced to play near their very best by a revamped Welsh side missing the likes of Sam Warburton, Ross Moriarty, George North, Justin Tipuric and Rhys Webb.
Wales might also have to go into next weekend's match against Georgia without the services of British and Irish Lions centre Jonathan Davies.
He turned his left ankle in the final play of the game and had to be carried off the field on the motorised stretcher and will be assessed during the week.
His injury came moments after replacement wing Hallam Amos had added a second home try to the one scored by Steff Evans in the first half.
"It looks like an ankle injury at the moment and he's been strapped up and put on crutches. It doesn't look brilliant, but we'll know more in the next 24 hours," said Wales head coach Warren Gatland.
“I'll think we'll make a lot of changes for next week. There will be some younger boys getting a chance.
"Some players who have been out of the squad a while will get an opportunity. It's a chance for players to put themselves in contention for the All Blacks game.
"It's about assessing where this group is in the next 48 hours and seeing how they come back on Monday."
When they do come back in they will have to reflect on a 13th successive defeat to the Wallabies, who are once again World Cup opponents in Japan in 2019, and be mindful of the fact the Georgians will arrive on the back of a 54-22 win over Canada in Tbilisi.
"We're disappointed in terms of the result, but we talked about throwing some new faces out there, some new caps. Some guys have had their first caps at home and they'll be better for that experience," added Gatland.
"That was Australia's ninth game in the last few months. If you look at where they started the Rugby Championship, they were beaten by 50 points by the All Blacks.
"Our whole focus is on planning for the World Cup – exposing some young players and giving them opportunities, developing the game that we can play.
"We've got Australia in our group and we have the next two years together to prepare for it.
"We'll go into that group with a lot of confidence."