Cueto, who is on the 15-day disabled list with a strained right lat, reported no issues a day after a 45-pitch bullpen session on Monday.
"He's fine. He came in and got treatment. He's strong," Price said. "Now it's just a matter of verifying that he's OK as opposed to just firing him off into a game, and there's still a twinge and you have to DL him again. There's a strong possibility that he'll make an outing or two in our player-development system to verify he's OK."
Because Cueto is very competitive and likes to push himself, the Reds will be deliberate in building his pitch count and making sure he doesn't try to rush back too soon. He is already eligible for activation at any time.
"We've got to do what we think is best for him," manager Dusty Baker said. "We also want to keep him on the field so he doesn't go back down again."
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.