Sanchez collapsed in obvious pain before the Trojans began stretching drills on Friday.
His injury came as he jumped while tossing a warm-up pass. He was later wheeled off the field before undergoing X-rays.
Sanchez was later diagnosed with a dislocated kneecap. He hopes to return for the Trojans' Aug. 30 opener at Virginia.
"Mark's injury is not as bad as a lot of people feared it was, so we'll take the reps until he gets back and we'll see what happens then," Mustain told the Los Angeles Times on Saturday after practice.
Corp, who passed for three touchdowns in USC's final drill on Saturday, said he's happy his teammate's injury is minor.
"I'm happy for Mark that the injury is not as serious as it could have been," Corp told the Times. "But my thinking hasn't changed at all. I'm still going to compete for first team reps.
"It's the same kind of opportunity, just shortened a little I guess."
Sanchez sat on a golf cart with his left leg elevated during the Trojans' walkthrough Saturday. He will begin rehab on Monday.
Sanchez said he fell asleep in the MRI exam machine after he was injured.
"I woke up and thought I was in a bad dream," he told the Times. "I was like, 'No!' And then it all sunk back in and I was like, 'Man.' But it could be a lot worse. I should be thankful."