General manager Dayton Moore is hoping for word next week prior to the March 31 season opener at Detroit.
Guillen, the right fielder and cleanup batter, stands to miss the first 15 days and 12 games for a violation of the Commissioner's drug prevention program.
Olivo, the backup catcher, faces a five-game penalty for fighting at New York last season while a member of the Florida Marlins.
Both penalties were appealed on the players' behalf.
The Olivo suspension, if upheld, means the Royals would have to open the season with 24 active players instead of 25. The Guillen penalty would not cost them a roster spot.
"It would be nice if we could know sooner or later, but I can't control that," manager Trey Hillman said. "I'm not frustrated with it, but the closer we get I do get a little more anxious. But I'm sure that's not at the top of their list to let us know something."
Moore is especially interested in the Olivo decision. That affects the number of players and could be a factor in whether the Royals will start the season with 11 or 12 pitchers.
Guillen's preparations were put a week behind by a flu bout, but if his suspension is lifted, he vows to be in top shape for Opening Day.
"When he's talked to me, the only thing he's said is, 'I'll be ready,' " Hillman said.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.