Morrow, who sustained a left oblique injury in a nine-pitch start on June 11, has one more rehabilitation start scheduled for Sunday with the New Hampshire Fisher Cats of the Double-A Eastern League before he returns to the Blue Jays.
He will be limited to about 85 pitches Sunday and also will have a similar limit for his first start back with Toronto. On Tuesday, Morrow threw 67 pitches (45 strikes) in 4 2/3 scoreless innings in which he allowed three hits and struck out six.
The Blue Jays have Monday off before opening a three-game series in Detroit, and that could factor in when Morrow makes his return.
If he pitches Friday, he would be going with the regular four days of rest.
"There's a possibility we could give him an extra day as well," manager John Farrell said. "So we've got some flexibility with this next turn through the rotation, particularly with Monday being an off-day. So it's not been set in stone yet. But we've got to get through Sunday first to really outline the first two series of the trip."
When Morrow does return, Farrell said he would still stay with a five-man rotation.
Morrow is 7-4 with a 3.01 ERA in 13 starts this season.