Price is expected to undergo a procedure to address a cyst in his left wrist, Speier added.
Cora also said the team will examine whether Price's wrist ailment goes beyond what is already known.
"We're going to see what's going on with his cyst and actually check his wrist," Cora said, according to Christopher Smith of MassLive.com. "If there's something else, we'll take care of that. If there's something going on. I think it's a head start to next year. It's a smart thing to do.
"If we were one game up or in the hunt, he'd probably be pitching out of the bullpen like in '17. But where we're at and obviously how important he is, it's better off moving forward and get him right."
The five-time All-Star will meet with doctors in the coming days, according to Smith.
Price landed on the injured list on Aug. 8. He has made one start since and pitched only two innings against the Seattle Mariners on Sept. 1.
The 34-year-old ends the campaign with a 4.28 ERA over 22 starts (107 1/3 innings).