Morrow hasn't pitched in the big leagues since straining his left oblique muscle during a start against the Nationals on June 11. He recently began a rehab assignment and has made three starts in the Minor Leagues, with another outing coming on Monday.
Following that appearance, Morrow likely will rejoin the Blue Jays but will be on a limited pitch count for at least his first couple of starts.
"Very likely," Blue Jays manager John Farrell said of a promotion. "We're looking at 65 to 70 pitches his next outing. So the fact we're carrying an extra pitcher right now, we could insert him in the rotation.
"We wouldn't increase the pitch count in his first time back here, so you know you're going to go in with a shortened start to begin with, but with the additional pitcher that we're carrying right now, we can handle that."
Morrow will become the second starter in the rotation that needs to have his pitch count closely monitored. Left-hander J.A. Happ recently made the transition from the bullpen and is not yet to the point of being fully stretched out.
Farrell said once both pitchers are back to full strength, he would consider going with a six-man rotation for the remainder of the season. That would help ease the burden on the staff and provide additional rest for right-hander Carlos Villanueva, who has experienced injury woes in the past.
A final decision on the rotation has yet to be made, but the club definitely won't expand its number of starters to six until Farrell is comfortable going back to a seven-man bullpen.
"Keep [the rotation] at five initially, because that kind of defeats the purpose of bringing [Morrow] back with a shortened pitch count, because you'd be overtaxing the bullpen again," Farrell said.
"Once he and Happ get stretched out to where they can go a minimum of 100 pitches, [I'd consider six], because if you're running a six-man rotation and two guys can only go 85 pitches, you're asking the bullpen to pitch an awful lot."