The Chicago White Sox don't consider anyone untouchable, but Rick Hahn would have to be blown away by a trade offer to make a significant move ahead of the July 31 deadline.

"Part of our responsibility is to stay in contact with clubs and find out how they value our players and see what opportunities there are for us to get better," Hahn said. "We don't hang up on anybody."

Chris Sale, Jose Quintana, Jose Abreu and Avisail Garcia are considered hard targets.

"A lot of times, you start off a conversation with them expressing interest in a player you may not be so inclined to move," Hahn said. "Based on their need, it leads to a different opportunity to make a deal that's a little more palatable. It doesn't make any sense to close off any conversation -- even if you know the odds are very long against anything happening on a certain player."