Morrison will go a full game either Friday or Saturday before beginning his rehab assignment with the Class A Hammerheads next week.
"If everything goes well on that, we'll figure out a date to start his rehab," Redmond said. "He feels good. He's progressing."
The 25-year-old is on the 60-day disabled list after undergoing right knee surgery last September. He is eligible to come off the DL as early as May 30.
Christina De Nicola is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.