Baird declined to state Greinke's problem.
"Out of respect to him, I'd rather have him do that," Baird said.
Greinke, when he does come back, probably will report to Arizona to make up for time lost when he left Spring Training. Then he'd probably pitch in the Minors before being ready again for Major League competition.
"He's doing good, sounding great, anxious to be back," Baird said.
"For the issues he's been going through, I'm really proud of him. He's a courageous young man."
Greinke is one of the Royals' brightest young talents. Their first-round draft choice in the 2002 First-Year Player Draft, he was called to the Majors in May 2004.
In his rookie season, Greinke had an 8-11 record and 3.97 ERA in 24 starts. However, last season he was just 5-17 with a 5.80 ERA in 33 starts.
With Runelvys Hernandez and Mark Redman also on track to return, the Royals rotation is likely to undergo an overhaul in the next few weeks.
Before Spring Training began, the Royals expected Hernandez, Greinke and Redman to take three of the five starting spots. But, after Greinke left, Redman had knee surgery and Hernandez was out of shape.
Redman is on the disabled list, scheduled to pitch for Double-A Wichita on Tuesday. Hernandez was optioned to Triple-A Omaha.
"Pitching wasn't the biggest issue," manager Buddy Bell said of Hernandez. "We know he can pitch. It's a durability issue and whether he maintains his stuff."
Hernandez got his first competitive test Sunday, pitching for Omaha against Nashville, and it didn't go very well.
In just three innings, Hernandez gave up eight runs on seven hits. He walked four and struck out one. Of 73 pitches, just 40 were strikes.
Even so, Bell didn't rule out Hernandez as Friday night's starter against Tampa Bay. That would hinge on a dissection of Hernandez's performance by Baird and the Omaha staff.
The Royals could decide to pitch Hernandez again for Omaha and start Mike Wood, Elmer Dessens or Jimmy Gobble against the Devil Rays.
"We've got options," Bell said, "but our preference is Runelvys."
Bye-bye, Buddy: When Bell was ejected in the ninth inning on Sunday, it was the fourth time he'd been tossed as the Royals' manager.
The last time came Aug. 10, 2005, against Cleveland.
DeJesus out: No surprise but center fielder David DeJesus was out of the lineup Sunday because of a strained left hamstring.
With Monday an open date, that means he won't return before Tuesday's first road game against the New York Yankees.
Against Chicago left-hander Mark Buehrle on Sunday, Bell put right-handed-hitting Tony Graffanino at first base instead of Doug Mientkiewicz.
Graffanino also led off, despite hitting just .214 (3-for-14) against Buehrle in his career.
Baird said that DeJesus' injury is not serious enough for him to go on the disabled list.
Reason to howl: Left-hander J.P. Howell held Nashville to two hits in six shutout innings of Omaha's 2-0 victory on Saturday. Howell struck out five with no walks.
Chip Ambres homered in the second game as Omaha completed a sweep, 3-2.
For Wichita, third baseman Alex Gordon was hitting .438 in three games, all losses.
Up next: The Royals are off on Monday. They'll open New York's home season on Tuesday at 12:05 p.m. CT at Yankee Stadium. They'll also visit St. Petersburg and Chicago on the nine-game trip. In those three ballparks last season, the Royals were 1-15. The only win came at Chicago, where they were 1-8.