Johnson, who played catch with pitching coach Bryan Price in the outfield here on Saturday, has thrown five bullpen sessions and was last on the mound a week ago Saturday when he threw 53 pitches.
After Monday's session, Johnson, recovering from offseason back surgery, will be reevaluated. Manager Bob Melvin has been reluctant to announced Johnson's schedule too far in advance.
"There's a good chance that the next one would be some kind of a game situation," Melvin said of Johnson's next step after Monday.
If Johnson were to take a normal four days' rest after Monday then he would pitch on Saturday. Whether that would be in the club's day game against the White Sox, a simulated game, or a B game, Melvin would not say.
The team is still looking for Johnson to be ready to pitch in mid-to-late April.
Sitting out: Outfielder Carlos Quentin still felt some soreness in his left shoulder after "tweaking" it while lifting a fly ball to left field on Friday night.
"It was just kind of an awkward swing, an emergency two-strike swing," Quentin said. "I was trying to foul it off. It's just a little tweak. It's not my throwing shoulder, so I could have finished the game if they had really needed me to. I'll listen to the trainers and take their advice."
That advice appears to be rest, though he is likely to have an MRI taken in the next few days.
"He had a little soreness early in camp with it and just kind of tweaked it with the swing," Melvin said. "You never say never, but my feeling is it's just day-to-day."
Progress: Dustin Nippert's start on Saturday wasn't a thing of beauty -- he allowed three runs on five hits over 3 2/3 innings -- but Melvin did see some positives.
"I liked the fact that he fought through it," Melvin said. "It's another time where he fought through some things where in the past he wasn't able to get through it, make some adjustments and pitch better later. Not the best overall results, but we're looking for progress with him and we've seen it the past two times."
One of the adjustments Nippert made was to throw his changeup more often to right-handed batters.
"I started throwing it and getting swings and misses and a couple of groundballs and it got me back in the ballgame," he said.
All he does is hit: Infielder Brian Barden may not be the favorite to nab one of the final two spots on the bench, but he's certainly putting together a solid case.
Barden was 2-for-4 with a double and a home run on Saturday to raise his spring average to .375.
Game notes: Catcher Chris Snyder started in the designated hitter slot in place of the injured Quentin and was 3-for-4 with a double and two RBIs. ... Conor Jackson hit a homer to center off Gil Meche. ... Scott Hairston lost a ball in the sun in left field in the first inning. "Arizona [sun] can be tough, but we don't use that as an excuse," Melvin said. ... Closer Jose Valverde followed up a strong session in a B game with one shutout inning. The right-hander allowed one hit while striking out two.
Up next: The D-backs return to Tucson on Sunday to take on the A's, with Livan Hernandez making his third start of the spring. Hernandez threw in a B game his last time out.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.