Price is in the process of returning from a left elbow strain he sustained on Feb. 28.
Another test will come when Price starts throwing breaking balls off the mound. He has already been doing so on flat ground.
"Different throw," Price said of breaking stuff. "Adds more stress to the elbow and everything else."
To this point, Price has responded to every challenge presented to him.
"He's made steady progress," manager John Farrell said. "He's thrown with intensity. He's thrown consecutive days in terms of long toss. Three consecutive days for that matter. The way the response has been physically has been very positive."
Price could be cleared to throw to some batters -- perhaps batting practice or a simulated game -- in the days after Saturday's side session. But the Red Sox are taking it on a wait-and-see basis for now.
Price doesn't mind the gradual approach.
"Just take it day by day," Price said. "That's the biggest thing. This is essentially Spring Training all over for me. I want to get through today and make sure I feel good tomorrow."
• Setup man Tyler Thornburg (right shoulder impingement) was able to initiate a throwing program for the first time since his shutdown towards the end of Spring Training.
"He threw out to 60 to 70 feet, first day of his throwing program and it was roughly 30 throws so it was just initiating his throwing program," Farrell said.
Ian Browne has covered the Red Sox for MLB.com since 2002. Follow him on Twitter @IanMBrowne and Facebook. This story was not subject to the approval of Major League Baseball or its clubs.