Guillen has appealed his suspension, which would keep him out of 12 games.
"I am sure hoping it gets wiped out," manager Trey Hillman said. "I don't think any manager would say anything contrary to that. I hope it'll get wiped."
Guillen received his penalty for violating baseball's drug policy under rules implemented in 2004 and 2005.
It came just hours after the Royals announced that Guillen had signed a three-year, $36-million contract.
"I ask players this all the time. Where would we be without that word 'hope'? Yeah, so I'm hoping that happens," Hillman said. "That would be wonderful."
Refining the timetable: Hillman said that second baseman Mark Grudzielanek likely will play his first game on Friday against the Colorado Rockies.
He and Guillen are being held back as veterans who can get ready at their own pace. Guillen might play next Sunday against the Chicago Cubs.
"And I'm hopeful maybe even sooner than that, but we'll see how his body is feeling," Hillman said.
Shealy returns: First baseman Ryan Shealy returned to workouts on Sunday after missing three days because of the flu.
Outfielders Justin Huber and Chris Lubanski were out on Sunday as they battled the bug.
"I'm just glad to get out of my house," Shealy said. "Huber called me and said his back hurt. I said, 'You better get off your feet and into bed.' "
Hillman said the lost days should not hinder Shealy's bid to make the roster.
"We've still got time. If anybody is going to get sick, it's better to get sick early rather than late when it's coming down to cutting the roster and making decisions."
Shealy began feeling woozy during the drills and left the ballpark about noon to return home.
Pitcher John Foster received an epidural injection in his back and is out for an undetermined period. Another left-hander, Mike Maroth, missed his first outing on Saturday because of a stiff left shoulder, but that appears to be minor.
Everyone in fold: The last five unsigned Royals have agreed to contract terms. They are infielders Shealy, Billy Butler and Alex Gordon, outfielder Joey Gathright and pitcher Brian Bannister.
Razor's edge: Hillman came to Arizona on Feb. 5 with a beard and mustache. It came off about three weeks later for the annual "photo day." For the last week, the grizzled look was returning to Hillman's visage, but on Sunday he was clean-shaven again.
It wasn't a Sunday-go-to-meetin' look.
"We had church inside [the clubhouse] but we have another picture that they threw at me so I needed to shave," he said.
Manager's take: After three games and before Sunday's rematch with the Rangers, here's how Hillman viewed his Royals' performance:
"I've liked the way we've run the bases and I've liked the defensive outfield play. I've liked the way we've created some opportunities to score some runs, and overall the hitting has been OK. It hasn't been great, it hasn't been horrible. I'm not pleased at all with the pitching, and I'm not pleased at all with the infield defense and just playing catch," he said.
Up next: The Royals will meet the Chicago White Sox at 2:05 p.m. CT on Monday at Surprise Stadium. Three of the five Royals pitchers will be left-handers -- starter John Bale, Jorge De La Rosa and Ron Mahay. Also scheduled are righties Yasuhiko Yabuta and Joakim Soria. Chicago's starter will be lefty John Danks, followed by Ehren Wasserman, Bobby Jenks, Boone Logan and ex-Royals Mike MacDougal and Octavio Dotel.