Speight is one of four uncapped members in the squad, with Western Force tighthead prop Tetera Faulkner and centre Kyle Godwin, and Melbourne Rebels winger Tom English.
Melbourne Rebels backrower Luke Jones has also received a call-up, after making his international debut for Australia in the second test against France in June.
Brumbies centre Matt Toomua is out after receiving a head knock in Australia's last game against Argentina in Mendoza, and Beale will not been considered until after a code of conduct hearing.
McKenzie will finalise his 23-man matchday squad next Tuesday but welcomed Cooper's return.
"You're always searching for the right balance of experience and youth in a squad, so it's pleasing to see Quade Cooper available once again and also a number of potential debutants putting their hand up for selection," he said.
Wallabies squad
Ben Alexander, Tetera Faulkner, Sekope Kepu, Benn Robinson, James Slipper, Saia Faingaa, James Hanson, Josh Mann-Rea, Sam Carter, James Horwill, Rob Simmons, Will Skelton, Scott Fardy, Scott Higginbotham, Matt Hodgson, Michael Hooper (c), Luke Jones, Jake Schatz, Will Genia, Nick Phipps, Nic White, Quade Cooper, Bernard Foley, Kyle Godwin, Tevita Kuridrani, Christian Leali'ifano, Adam Ashley-Cooper, Tom English, Israel Folau, Rob Horne, Henry Speight, Joe Tomane
- AAP