The club would like Iglesias to test his arm in a side bullpen session soon.
"If we get through that, I think we can talk seriously about penciling him in maybe for a start at some point before the season is out, or at least an appearance," Price said.
Iglesias, 25, is 3-7 with a 4.18 ERA in 18 games, including 16 starts. In 95 1/3 innings, he's allowed 81 hits and 28 walks with 104 strikeouts and a 1.14 WHIP.
The Reds have been careful with Iglesias because of his limited pitching the past couple of seasons. He worked only seven innings in the Arizona Fall League last year because he spent the season in Haiti awaiting a visa following his defection from Cuba.
A date for the proposed bullpen session has yet to be set, nor have the parameters of what Iglesias would need to do to get the green light to return to game action.
"I'm optimistic that he will take the mound again this year," Price said. "In my opinion, the only reason he wouldn't is being just extremely cautious. I didn't think there is anything medically that would prevent him from being able to go out and pitch."
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, follow him on Twitter @m_sheldon and Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.