Recently returned from an overseas stint, Mumm was just as impressive off the bench in the victory against Argentina in Mendoza.
Horwill appears to be the frontrunner after training alongside the majority of starters from the Argentina test.
"I know it's disappointing for Rob [Simmons] and he really wanted to play but I just think it is a great chance for someone else," Cheika said.
"I just think if you get the opportunity to play for Australia in a test match here against New Zealand, someone is going to get a lucky call and it's an opportunity for that guy to make the most of it."
Cheika said inside back Matt Toomua and prop James Slipper, who suffered head knocks against Argentina, would be available to play if they came through their contact session today without any dramas.
Flanker Michael Hooper will play on Saturday after a Sanzar appeals committee dismissed an attempt to stiffen his recent ban for foul play.
- AAP