Price has been sidelined since July 28 with left elbow inflammation.
The 2012 American League Cy Young Award winner began the season on the disabled list with a left elbow strain before returning on May 29. He posted a 5-3 mark with a 3.82 ERA in 11 starts before making another trek to the disabled list.
"(He) recognizes the limited available of time to build back up, so logically this is a spot and he's accepting of the role," manager John Farrell said of Price's expected role in the bullpen. "He wants to get back and pitch. He wants to get back and compete."
Price has sparred with the media this season, including a much-publicized incident in which he lashed out at Hall of Fame pitcher and current NESN TV analyst Dennis Eckersley on the team plane June 29.
The 32-year-old Price mocked Eckersley and cursed at him multiple times during the confrontation, the Boston Globe reported.
Price has notched a 22-12 record in 46 starts since joining the Red Sox in 2016. He has a 126-68 mark with a 3.24 ERA in 264 major league appearances (259 starts) with the Tampa Bay Rays, Detroit Tigers, Toronto Blue Jays and Red Sox.