Morton is slated to throw either seven innings or 90 pitches for Class A Advanced Bradenton in Port St. Lucie, Fla.
It will be Morton's first competitive game outside of extended spring action since an April 4 exhibition in Philadelphia in which he walked five batters and threw two wild pitches in 1 2/3 innings.
After undergoing offseason surgery on his right hip, Morton returned to full health this spring but struggled with his command as he attempted to sync up his delivery.
The Pirates sent Morton to extended spring camp in Bradenton, Fla., where he progressed from bullpen sessions and simulated games to competitive games. His most recent outing came Monday, when he threw about 75 pitches in six innings.
"All in all, I think it was a positive outing," Hurdle said. "I think the reps were good, the volume of pitches was good. He had a very candid, open conversation with [pitching coach Ray Searage]. We watched the video."
Hurdle said the Pirates weren't yet sure how many rehab starts Morton will need to make before rejoining the Major League team.
"We're taking 'em one at a time," Hurdle said.
In other injury news, right fielder Gregory Polanco remained sidelined Tuesday night because of tightness in his left groin, but he said he felt better after a day of rest and treatment, though he did pinch-hit in the eighth inning.
Polanco took pregame batting practice with the Pirates before Tuesday night's game at Wrigley Field. He was scratched Monday due to the injury, which he aggravated while legging out a double in his final at-bat Sunday in Arizona.
Polanco tried to get loose enough during Monday's warmups but couldn't.
"It's hard to warm up here in this cold weather," Polanco said. "I'll be fine."