Cooper was included in McKenzie's initial 40-man squad for the upcoming Rugby Championship campaign.
The 25-year-old played the last of his 38 Tests against Argentina in September last year before falling out with former coach Robbie Deans after labelling the Wallabies environment "toxic".
He was left out of the British and Irish Lions series but is almost certain to start in the number 10 jersey in the Bledisloe Cup and Rugby Championship opener in Sydney on August 17.
"I don't worry about Quade under pressure at all," McKenzie said.
"You have to look at the circumstances, I know the conversation that everyone talks about (Cooper's poor performance at the 2011 World Cup), but I think I could have a look across the board at plenty of other players that haven't played their best football on a certain day somewhere.
"All I'll say about Quade is he's been very good at delivering what I've asked him to do over the years, so I don't have a problem with that."
Brumbies young-gun Matt Toomua and uncapped Waratahs playmaker Bernard Foley are the other specialist fly-halves included in the 40-man squad.
Troubled star Kurtley Beale will miss the entire Rugby Championship with a shoulder injury, while McKenzie confirmed he's planning to play incumbent Test number 10 James O'Connor on the wing or at full-back.
"When you're carrying a shoulder injury for a long period of time and it's having an impact on your game, we felt the best thing for Kurtley was to get it fixed," McKenzie said.
"And by doing it now that allows him the opportunity of a pre-season so he can come back in and hopefully play a fair bit of Super Rugby that would lead him into being 100 per cent fit to be able to play Test football next year."
The squad will be trimmed to 30 players on August 9 ahead of their tournament opener against New Zealand in Sydney on August 17.
McKenzie has overlooked utility Berrick Barnes and lock Sitaleki Timani, who are both heading overseas at season's end.
However, code-hopper Israel Folau, who is yet to commit to rugby beyond this season, has been named.
Asked if he's confident Folau is poised to commit until the end of the 2015 World Cup, McKenzie said: "There's still negotiations going on there and I'm not privy to the negotiations but I wouldn't have picked him if I wasn't confident that he'd still be there."
Meanwhile, McKenzie said he's comfortable starting his Wallabies coaching career with back-to-back games against the world champion All Blacks.
"In a perverse way I'm quite happy with the start," he said.
"I relish the opportunity to be involved against the All Blacks. I had lots of encounters as a player and as an assistant coach so I really look forward to it.
"When you tackle the team that everyone recognises at the number one side, that's your biggest opportunity to go forward.
"I can't think of a better scenario actually where you've got two games against them in a row.
"So the Bledisloe Cup's right there and in seven days you can do a lot, you can change the shape of a lot of things if you get it right."
Wallabies squad: Ben Alexander, Adam Ashley-Cooper, Peter Betham, Quade Cooper, Nick Cummins, Dave Dennis, Kane Douglas, Anthony Fainga'a, Saia Fainga'a, Scott Fardy, Chris Feauai-Sautia, Israel Folau, Bernard Foley, Will Genia, Liam Gill, Mike Harris, Michael Hooper, James Horwill, Sekope Kepu, Peter Kimlin, Tevita Kuridrani, Christian Leali'ifano, Ben McCalman, Hugh McMeniman, Jesse Mogg, Stephen Moore, Ben Mowen, James O'Connor, Nick Phipps, Tatafu Polota Nau, Hughe Pyle, Benn Robinson, Paddy Ryan, Jack Schatz, Rob Simmons, Scott Sio, James Slipper, Joe Tomane, Matt Toomua, Nic White.
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- Rugby Championship
- Quade Cooper
- Matt Toomua