Morrow, who underwent shoulder surgery in October, could be ready for game action by mid-to-late April.
"He's getting onto the mound a little quicker than I anticipated, which is nice," said manager Andy Green, "but it's going to be a stretch to get him ready for the start of the season."
Morrow will go through the same progression that the club's other starters did earlier this spring, putting him approximately three weeks behind schedule. With that in mind, the Padres will most likely opt to keep him in Arizona once the season begins to continue increasing his workload.
San Diego also has the benefit of an off-day on April 7 after its opening series vs. the Dodgers.
"Technically, you don't need a fifth starter until April 13, if we're going to be looking at it that way," Green said. "There's still a 25-day window right there for him to get ready for the season.
"But all of that's going to be dependent on how he feels, and we don't want to push him too quick."
Morrow opened last season in the rotation and made five impressive starts, posting a 2.73 ERA and 1.09 WHIP. But he's been bit by the injury bug throughout his career, with six stints on the disabled list. He hasn't reached the 150-innings mark since 2011, with Toronto.
• Opening Day starter Tyson Ross was as dominant as you'd expect in five innings against Mariners Minor Leaguers. He struck out nine -- including five of the first six batters he faced -- and allowed just an unearned run on three hits and a walk.
With Ross set to face Los Angeles for the April 4 opener, the Padres opted to use him in the Minors instead of giving the Dodgers a live look at his pitches.
AJ Cassavell is a reporter for MLB.com. Follow him on Twitter @ajcassavell. This story was not subject to the approval of Major League Baseball or its clubs.