Cervelli, who was placed on the 60-day disabled list with a strained right hamstring back in April, is currently with Double-A Trenton and has played in six Minor League rehab games. He hasn't appeared in the big leagues since April 13.
"We'll make an evaluation after tonight, see where he's at," Girardi said. "We feel that he's pretty healthy, and that's a great sign. It could be when we get back. We'll see where we are after tonight and evaluate it every day."
Girardi indicated that the Yankees plan to start Brian McCann in all three games against the A's in Oakland. Murphy was the beneficiary of Cervelli's absence, taking over duties as McCann's backup, and he has impressed.
The 23-year-old Murphy entered play on Thursday batting .296 (16-for-54) with a home run and eight RBIs in 21 games, while also showing good defensive ability. Girardi said that it could be beneficial for Murphy to play every day.
"I don't think it ever hurts anyone to play every day, to develop," Girardi said. "You get in a rhythm more, and I think you can learn more about yourself, physically, sometimes if you're playing and your career is to be an everyday catcher. I think that's important to do, to learn how to handle fatigue and all those different types of things."
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.