Morrow has been on the disabled list with a strained left oblique muscle since June 12. He is expected to be out until at least mid-to-late August, but a pain-free bullpen session indicates that he is at least on schedule.
"[Morrow] threw all of his pitches, no ill effects today," Blue Jays manager John Farrell said. "He's scheduled for another [bullpen session] on Thursday. I would assume -- and tentatively scheduled -- for the same number of pitches, maybe a few more.
"That would put him in line for batting practice, likely a week from today."
Morrow will require three-to-five rehab starts in the Minor Leagues before being able to make a return to Toronto. His presence would be a welcome addition for an injury-riddled starting staff that is also without Drew Hutchison and Kyle Drabek.
The 27-year-old Morrow was enjoying a career year at the time of his injury. He is 7-3 with a 3.01 ERA and three shutouts in 13 starts this season.