Toronto's No. 2 starter is scheduled to throw a bullpen session on Tuesday and two days later he'll report to the club's Minor League complex in Dunedin, Fla., to begin his rehab.
"I'll throw another bullpen in Florida when I get there and two or three games, it's undecided yet, depending on need, pitch count, all of that," Morrow said. "Conservatively it would be three [rehab starts], and if they feel like they want me back on a 75-80 pitch count then I would be back after two."
If Morrow does require three starts before a return, he likely won't be back until early July. The timetable could be longer if there is any type of setback, but that's something Morrow is hopeful to avoid.
The 28-year-old is 2-3 with a 5.63 ERA in 10 starts this season. He previously missed a start earlier in the year with tightness in his upper back and neck, but this marks his first stint on the disabled list in 2013.
"Each day has been better as far as finding my arm slot again and ball coming out," Morrow said. "Today, I felt as good as I have all season."
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, and follow him on Twitter @gregorMLB. Teddy Cahill is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.