Multiple media outlets reported Wednesday that Crawford was visiting well-known orthopedic surgeon Dr. James Andrews in Birmingham, Ala.
"He's feeling so good with his hitting and his wrist right now that he doesn't want to have any setbacks," Valentine said. "I think he might even get somebody else to confirm that it is what we think it is, which is just a little soreness. I'm not going to medically describe it. I don't know what it is."
Crawford had offseason left wrist surgery in January and then developed inflammation in it when he reported to Spring Training.
The Sox's left fielder returned to Fort Myers, Fla., on Tuesday night, and Valentine is unsure when the second opinion will take place and who will examine Crawford's elbow.
Crawford has not started throwing or playing in Minor League rehab games. He's been limited to designated hitter work in extended spring games and was in Boston during the team's first home series against the Rays because of the elbow soreness.
Is the injury serious?
"It's always serious, the way I look at it," said Valentine. "It doesn't seem major, if that's what you mean."