While general manager Ben Cherington confirmed that the Red Sox have interest in the 27-year-old Castillo, he isn't tipping his hand on the chances of acquiring him.
"There's obviously been attention on this," said Cherington. "He's a player that we've seen and have talked to, but we're just one of several teams that have done that. There's nothing more I can say than that."
Castillo is known for having a combination of power and speed.
"I'm not going to get into our evaluation in public," said Cherington. "Again, we've seen him, we've talked to him and we're one of several teams that have done that. There's not really anything else I can say."
The Red Sox were heavily involved in the sweepstakes for Jose Abreu, who wound up signing a six-year, $66-million deal with the White Sox and has been an impact player in his rookie year.
Boston also scouted Cespedes right before he went to the Athletics, but the ability of Cuban players to transition quickly wasn't as well established then.
"I think he's surprised everyone in the industry probably with just how quickly he made the transition to the big leagues when he signed initially," Cherington said of Cespedes. "And we've had more examples of high-profile Cuban players come out since then, so maybe we're more informed now on what that transition is like."
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. This story was not subject to the approval of Major League Baseball or its clubs.