Mesoraco underwent an MRI, which did not indicate a serious issue, and is rehabbing at Reds medical director Dr. Tim Kremchek's facility.
To have coverage behind the plate, the Reds called up Kyle Skipworth from Double-A Pensacola on Monday to back up Brayan Pena. The disabled list is not an option at this point, Price believed, because Mesoraco isn't expected to miss too much time.
"I think we have to see how he comes through the treatment. He was a bit better today," Price said. "Certainly, Dr. Kremchek and [physical therapist Christy Sweeney] back in Cincinnati will have a lot more to say about that. At least the initial report was that this wasn't something that [is] a disabled-list deal.
"There's a possibility that at any point in time, he could be here to play -- be it here or in St. Louis."
Mesoraco, who signed a four-year, $28 million contract in the offseason, is off to a slow start in 2015. Batting .095 (2-for-21) in six games so far, he dealt with a couple of Spring Training injuries, including a concussion that put him out for a week and a cramp in his left quadriceps.
The club felt it was better for Mesoraco to stay in Cincinnati for rehab rather than be on the road trip.
"There's no reason for him to be here, or in St. Louis, if he's not ready to play," Price said. "They have way better facilities than you'll find in a visiting clubhouse as far as contributing to his rehab."
• In other injury news, pitchers Keyvius Sampson and Matt Magill have been throwing simulated games in extended camp in Arizona. Both pitchers, who were optioned to Triple-A Louisville on March 20, had been shut down for a couple of weeks with elbow inflammation.
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.