Bailey was examined in Boston on Monday, and manager Bobby Valentine said the right-hander would receive a second opinion on Tuesday. That second opinion will come in Cleveland, the Globe reported, with specialist Dr. Thomas Graham.
"I think he's seen one [doctor]," Valentine said Monday afternoon. "Now we'll go and get another opinion, just to make sure."
Surgery could come as soon as Tuesday, the report said.
Mark Melancon and Alfredo Aceves are the two favorites to replace Bailey if he's out.
Bailey threw 26 pitches in a Minor League contest Wednesday, but he hasn't appeared in a Grapefruit League game since March 25. The Red Sox aren't sure when he injured his right thumb, but it's possible it happened when he collided with the Pirates' Alex Presley at first base during a March 21 game.
Bailey first noticed the injury while squeezing a shampoo bottle a day or two after the Pirates game.
"A couple days later, he was squeezing some shampoo, and said, 'Man, my thumb is sore,'" pitching coach Bob McClure said. "You have stuff that's sore all the time. It's like, 'Well, you know, big deal. It'll go away.' It just didn't go away."
The right-hander started the season on the disabled list last year with Oakland because of a forearm injury, and this year, he didn't make his Grapefruit League debut with the Sox until March 12 because of a lat injury.
In six Grapefruit League appearances, Bailey went 0-1 with a 4.50 ERA, notching seven strikeouts and allowing just one walk. Bailey hasn't had more than 50 regular-season appearances in each of the last two seasons.