"I'm good to go, I believe," Mesoraco said. "I don't know what the official plan is yet, but they want me to go play a few games somewhere."
Mesoraco practiced tagging up, secondary leads and short sprints.
"I don't feel anything; it feels perfectly good," said Mesoraco, who strained his left hamstring on April 25. "There are no worries at this point."
Mesoraco was eligible to be activated from the 15-day disabled list on Sunday, but as of Saturday that was not expected to happen.
"I would say that's extremely unlikely," Reds manager Bryan Price said. "As early as next week, he could be playing, at least in a rehab game or two. That's probably going to be part of the equation just to validate that he's OK."