Morrow experienced some discomfort in his back while throwing a side session earlier this week, but the Blue Jays don't expect it to become a major cause for concern.
When asked if Morrow would definitely start on Sunday, Blue Jays manager John Gibbons said, "We think so, no reason not to at this point."
The injury is being reported as minor, but there will still be a level of skepticism about Morrow's availability to pitch in Boston.
The doubts are a natural reaction after previous injuries to Josh Johnson and Sergio Santos were also described as minor, and eventually resulted in stints on the disabled list despite the club's previous claims.
Morrow got off to a slow start, but his effectiveness has increased in recent outings. He last pitched on May 5 against Seattle, and threw eight innings while allowing two runs on three hits and striking out eight.
The eight innings were the most thrown by a Blue Jays starter this season, and Toronto can ill afford to lose him for any period of time. The club is already without Johnson and left-hander J.A. Happ, which has exposed a lack of depth in the Minor Leagues.
Right-hander Ramon Ortiz is scheduled to take the mound on Friday night in Morrow's absence. The 40-year-old is 2-0 with a 2.18 ERA in four games with Triple-A Buffalo, but has thrown only 3 1/3 innings at the big league level in the past two years.
Just how long Ortiz remains with the club remains to be seen. He was chosen for the spot start mostly because the decision had to be made on short notice, and Ortiz was one of the only candidates who had proper rest.
But there's no guarantee that the start will be handed to Ortiz next time through the rotation.
"He's had some success," general manager Alex Anthopoulos said. "In fairness, he does have a two ERA down there. He's been here before. He's had success, he throws strikes. And if not him, you probably go with someone who's maybe a day off his rotation."
The Blue Jays currently have a four-man rotation of R.A. Dickey, Mark Buehrle, Morrow and Ortiz after Ricky Romero was optioned to Triple-A Buffalo Thursday morning. With a pair of off-days looming next week the club won't need a fifth starter until May 21.