"He's been out at Beacon Medical while we've been on the road. He's been working hard," Price said. "Now that he's throwing ... we can really monitor how he's throwing, the duration and things of that nature."
Cueto threw again on the field, this time at Busch Stadium, on Monday afternoon. He has been making steady progress.
"He's throwing like he's never been injured," Price said. "However, it hasn't been until we've gotten back to the mound when at times he's started to feel the discomfort. We are just trying to be cautiously optimistic that his worst days are behind him."
As for the days ahead, it remains to be seen if Cueto can get ready in time to help the Reds in the stretch run or postseason. He has yet to throw from a mound.
"I really don't know. He thinks so. That's where it starts," Reds manager Dusty Baker said. "It would be big, whether we got him back starting or relieving."
The Reds are keeping an open mind, thus far, about the type of role Cueto would return to for this season.
"The only thing we can really look at right now is the progression that he makes, how much time we're going to have in the season by the time he's ready to start a rehab assignment," Price said. "If we're getting into the second half of September before he's going out on a rehab assignment, it'll be difficult to get him ready as a starter.
"However, we have to try and get him as much work as we can over the course of the time we have left and see what our options are. We might be able to stretch him out enough to start in that amount of time. We don't know that yet."
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, and follow him on Twitter @m_sheldon. This story was not subject to the approval of Major League Baseball or its clubs.