The Red Sox will wait to see how he feels on Wednesday before outlining his plan going forward, but the lefty could start his Minor League rehab assignment Sunday.
"It could be," Red Sox manager John Farrell said. "With all fairness to David, we'll make sure he comes in tomorrow as he's been doing, and that would give us the opportunity to have a conversation and lay out where he's going from there. The next work session would be on Sunday."
Price faced teammates Jackie Bradley Jr., Deven Marrero and Chase d'Arnaud, and mixed in all of his pitches. It has been a long road back for Price since suffering a left elbow strain on Feb. 28, but his return seems to be within sight.
A best-case scenario would have Price pitching for the Red Sox by the final week in May.
"It's good to see him at the point now, where it's a matter of fine-tuning to execute pitches as opposed to always being a physical response to the workload," Farrell said. "A good workday for him. Would anticipate a light bullpen on Thursday as he's been doing, and then we'll see where we go after that."
Sandoval suffered a right knee sprain on April 25 and has made strong progress in recent days.
"With Panda, he's taking BP today in the cage. That's regular BP, not just hitting off a tee," Farrell said. "I would hope in the coming days he'd be out on a rehab assignment as well. The swelling's gone."
The injury to Sandoval was magnified given the lack of production and rash of injuries the Red Sox have had at third base. Brock Holt and Marco Hernandez are also on the disabled list. Josh Rutledge, who opened the season on the DL, is the latest to get a chance to start at third for Boston.
• Hanley Ramirez will play defense for the first time this season when he starts Wednesday's game at first. This will mark Mitch Moreland's first time out of the lineup this season. Ramirez hasn't been able to play defense due to a right shoulder injury.
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.