Ellsbury has played only nine games this season because of four broken ribs. He will be checked by Dr. Lewis Yocum on Wednesday in Los Angeles at the Kerlan-Jobe Clinic.
Ellsbury, who led the majors with 70 stolen bases last season and batted .301, was hurt in a collision with Boston third baseman Adrian Beltre on April 11. He was out for more than a month, then returned for a week before going back on the disabled list.
Ellsbury has undergone a series of tests, but is still feeling pain and isn't close to returning. He and his agent, Scott Boras, want another opinion on the injury.
"He has permission to be examined thoroughly," Red Sox manager Terry Francona said before Tuesday night's game with Cleveland. "Whatever that entails, they kind of have our blessing. We need to try to get as much information as we can."
Francona doesn't mind that Ellsbury is looking outside the organization for another examination.
"I hope there isn't something new," Francona said. "If nothing else, get an opinion that's completely removed from everybody that's been around him. We don't know. That's why we're sending him."
Francona said Ellsbury, who's hitting .250 with two stolen bases and three RBIs this season, will rejoin the team this weekend in Boston.
Ellsbury worked out doing baseball activities on Monday and Tuesday at Progressive Field.