Toronto's right-hander is working his way back from a strained left oblique muscle. Earlier this week, he was temporarily shut down because of a back issue, but has since returned to form.
Morrow returned to the mound Saturday morning at the club's Minor League complex in Dunedin, Fla., and everything went according to plan.
"He threw a 42-pitch, all-pitch bullpen [session] and came out of it fine," Blue Jays manager John Farrell said. "He threw his 'pen on Saturday ... and came out of it feeling fine. So right now, we're probably looking at Tuesday or Wednesday as his [batting practice] session."
Morrow likely will repeat the step of facing live hitters a couple of times before going on an official rehab assignment. He is expected to make three to five rehab starts, which would put him in line for a mid-to-late August return.
Jose Bautista also has made positive strides as he attempts to work his way back from a sprained left wrist. Bautista suffered the injury on July 16 in New York while taking a swing against Yankees right-hander David Robertson.
The Toronto slugger is wearing a soft cast to protect the damaged area, but is making progress as he advances through various stages of treatment.
"Two days ago, went through some strengthening exercises with the hand, and as any injury would have, there's a little bit of stiffness that resulted from it," Farrell said. "But with treatment, it gets kicked out of there the same day. He has yet to do any rotational type work with his hand, but he's further along than any of the medical staff envisioned after that swing that night in New York."
Farrell added that it was still too early to say whether Bautista would require a rehab stint or if he would be ready once the 15 days on the disabled list expires on Aug. 1.