Garza said his throwing arm is fine, but conditioning is the real issue.
He also said he will not rush the healing process, and there is no timetable for him throwing off the mound. Garza, who did well in evaluations with the team's medical staff on Wednesday, said being ready for Opening Day is a big deal and getting healthy is the first thing.
The 29-year-old right-hander sustained the injury in drills on Feb. 17.
He had been working out during the offseason to rehab his right elbow, which ended his season last year because of a stress reaction. That injury kept him out for the last two months of last season.
Garza went 5-7 with a 3.91 ERA last season.
ESPNChicago.com's Bruce Levine contributed to this report and information from The Associated Press also was used.