Stauffer, who has been on the disabled list since May 15 with a right elbow strain, threw two bullpen sessions while the Padres were in San Francisco, and said he experienced "no issues whatsoever" after the second session, which included fastballs and changeups.
Padres manager Bud Black said Stauffer's Saturday session will also add breaking balls into the mix.
"From there, we'll evaluate his bullpens," Black said. "If he continues to progress at this rate, he's getting closer to a rehab game."
That rehab game, if things go as planned, will likely be by the end of next week. First, Stauffer needs to get through a couple of more bullpen sessions. After that, Black said the righty will throw an inning of rehab in Arizona before the team maps out a full rehab schedule for Stauffer.
While Stauffer is nearing a rehab outing, rookie pitcher Anthony Bass recently began a throwing program. Bass has been on the DL since June 24 with inflammation in his right shoulder.
"As long as he's throwing well, we're going to continue to ramp him up," Black said.
Black added that righty Andrew Cashner, who has been sidelined since July 4 with a strained right lat, is "still a ways away" from beginning a throwing program. The Padres currently have no timetable for Cashner's return.