Morrow and interim manager Pat Murphy sounded optimistic Tuesday that Morrow is headed toward another Minor League rehabilitation stint in the near future.
"I think he's going to continue to play, have some bullpens and do a simulated [game] and probably send him off to a rehab assignment," Murphy said. "It doesn't look like it's too far off."
Morrow, on the disabled list since May 3 with inflammation in his right shoulder, left a rehab start with Double-A San Antonio early on June 7 after experiencing discomfort in his shoulder. An MRI showed no structural damage.
After a period of rest, Morrow resumed playing catch Friday while the Padres played a series in Phoenix against the D-backs.