CHICAGO -- Left-hander José Quintana is moving closer to joining the Cubs' rotation, but the specific timetable remains under discussion.

On Tuesday, Quintana threw a bullpen session as the latest step in his comeback from a left thumb injury. Cubs manager David Ross noted Tuesday that Quintana was scheduled to throw one more simulated game before potentially being activated from the injured list.

And then?

"There may be a possibility that his next outing could be with us," Cubs pitching coach Tommy Hottovy said on Tuesday. "Again, we're still trying to determine over these next few days where everybody is."

Quintana worked four innings in a simulated game on Sunday at the Cubs' alternate training site in South Bend, Ind., and Hottovy noted that the lefty was able to focus more on pitch execution and sequencing without worrying about his hand.

With an off-day Thursday, the Cubs have the potential flexibility to not need a fifth starter until Aug. 25 in Detroit. Theoretically, Quintana could slot into the rotation spot that opened this past weekend when righty Tyler Chatwood landed on the 10-day IL with a back strain.

Hottovy said Chatwood is seeking more details on his back issue and the team should have more information in the coming days.

Miller's first time
Righty Tyson Miller said his two-inning Major League debut in Game 2 of Monday's doubleheader against the Cardinals was "special, for sure," adding that it will feel like a second debut when he has a chance to pitch in front of fans at Wrigley Field.

Ross mentioned that Miller was able to test out a couple "new toys" that he has worked on at South Bend. Hottovy offered more details, explaining that Miller has added a two-seam fastball and two-seam changeup to balance the rest of his pitch mix.

"He's such a good kid. He's a good athlete," Hottovy said. "He can do so many different things with a baseball. It's a really unique look what he brings to the table. And then being able to add just a few more pitches to that mix to kind of round it out will help him, for sure."

Worth noting
• Ross has been reluctant to apply the "closer" label on any of his late-inning relievers, preferring to maintain flexibility with the group. Hottovy agreed that was the best approach with Craig Kimbrel, Jeremy Jeffress, Rowan Wick and Co. right now.

"I do absolutely believe right now that's the best way to go," Hottovy said. "I think just having a group of guys out there that you trust and that want the ball in any situation is just going to lead to us having more success. And I think those guys understand that we trust them all in a lot of different situations."

• Righty Adbert Alzolay recently sustained a right forearm contusion on a comebacker in an outing in South Bend. Hottovy said the starter is doing better and is "definitely an option" for Wednesday's doubleheader. With the Thursday off-day, though, Chicago is still discussing how it will handle the twin bill.

• Per historian Ed Hartig, Game 2 on Monday was the first time the Cubs batted first in their home ballpark since July 16, 1908, against the Giants at the West Side Grounds. The Cubs and Cardinals will play under the same format in Game 2 of Wednesday's doubleheader.

Quotable
"You know, 3-0, I want my best players swinging as often as possible, to be honest with you, if they've got a plan. ... With a seven-run lead, I'm probably not even looking at my coach and telling the guys take or not. I'm just letting the game play out at that point. You've got a lead, you're safe. If the guy wants to swing, I don't have a problem with it." -- Ross, on the conversation surrounding Padres shortstop Fernando Tatis Jr.'s grand slam on a 3-0 pitch against Texas on Monday