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6/19/2013 8:18 P.M. ET

Trade Deadline groundwork beginning in earnest

MINNEAPOLIS -- White Sox general manager Rick Hahn met with the media Tuesday as talk of the July Trade Deadline already dominated the conversation.

Hahn noted that he has already started to receive some calls -- as is usual once the First-Year Player Draft is over -- and especially with the position the White Sox are in, nine games out of first in the American League Central at the start of play Wednesday.

"Given the way we've played thus far, it's not a real surprise we've had some phone calls -- more of the vulture-type phone calls, the type that traditionally we're more accustomed to making," Hahn said. "But that's part of the hole that we've dug for ourselves, that teams are going to look at us as potential sellers when the Deadline comes, and they're starting to lay a little bit of that ground work now."

Hahn didn't want to assess the potential movement of any individual players, especially with so much time left before the Deadline. He did say that regardless of how the next six weeks go, they will have "25 guys in that clubhouse every day and a coaching staff every day that's focused on winning that night's game."

But to deal with hypotheticals about any individual player would distract the White Sox from trying to turn their season around.

Paul Konerko added that the potential for a team to lose certain players in a trade is simply a part of the game players have to deal with.

"When it comes to that kind of stuff, I don't want to say you can't control those things because you can obviously as a team and as a player going on the field, [you] can control it in a way," Konerko said. "But all you can do is your best, and that's what we've been doing. I think everybody knows and is mature enough in here. … You just know going into it with this job that the management will make moves if they see fit at any time to do that."

White Sox bullpen back at full strength

MINNEAPOLIS -- After working with a short bullpen by choice Tuesday, the White Sox had their full set of relievers available Wednesday.

White Sox manager Robin Ventura decided to give right-handers Jesse Crain and Nate Jones a rest after some extended outings in recent games. In 29 appearances this season Crain has thrown 31 2/3 innings with a 0.57 ERA. Jones has 33 appearances with 36 innings and a 5.00 ERA.

"We played so many games that are like that," Ventura said. "You're either going to use them every night or you're going to have to find out about [Ramon] Troncoso. Or even with [Matt] Lindstrom. … Tonight, they're available."

As Ventura noted, by sitting Crain and Jones, he afforded some other relievers -- most notably right-hander Troncoso on Tuesday -- the chances to show where they can be helpful. Troncoso entered Tuesday night's game in the seventh inning with two outs. He threw 1 1/3 innings, during which he gave up two runs on two hits and was credited with his second loss of the season.

While Crain and Jones are Ventura's go-to men in close games, the White Sox have played 25 one-run games this season and are 10-15 in those contests. With the possibility of facing a one-run situation frequently, Ventura needs more options late in the game.

"We're going to have to find, to see what other guys are able to do," Ventura said. "You have to use your whole bullpen. I think the way it's been going, we play tight games anywhere, so they're either going to be used any night or you're going to have to find out who we have down there and what they're capable of doing."

Ventura looking to give Alexei a break

MINNEAPOLIS -- White Sox shortstop Alexei Ramirez continues to be an everyday feature of the White Sox lineup, as he made his 69th start in the team's 69 games this season.

Ramirez hasn't missed a game all year but before the first half is over, White Sox manager Robin Ventura said he'd like to give his shortstop a day off, but he can't positively say when or if it will happen.

"I think it'll help," Ventura said. "You would like to, but you can't guarantee that. You'd like to get him a day somewhere in here that you can -- maybe even get in around one of those off-days, so you can make it an extra day.

"It might not happen, but I think right now if we were able to do it, Gordon [Beckham] would go over to shortstop."

Kelly Erickson is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.