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7/14/2013 7:00 P.M. ET

Danks wants to finish unfinished business with Sox

PHILADELPHIA -- There were times during John Danks' injury plagued 2012 season and then his 2013 comeback from season-ending arthroscopic shoulder surgery last August where he wasn't sure if the White Sox would still be interested in him, let alone other teams.

But as the July 31 non-waiver Trade Deadline approaches and the White Sox move closer to elimination than playoff contention, the left-handed starter remains one of the handful of players drawing interest from other teams. Danks, 28, has enhanced that interest with four straight quality starts, working 27 2/3 innings during that stretch, and walking eight in total all year over 62 2/3 innings.

The good news concerning Danks is that pitchers tend to hit their full stride somewhere around 18 months after surgery, and Danks already looks strong on the mound. He also is under contract for the next three years in his five-year, $65 million deal.

As the All-Star break approaches, though, Danks sounds like many of his teammates. He's disappointed in the team results, but doesn't want to leave Chicago.

"Yeah, this is where I want to win a World Series. I want to play my whole career here," Danks said. "This is where I'm comfortable. I know the people and it's fun. This is where I want to be. But it's part of the game and if something happens, something happens."

To be honest, Danks is more worried about getting better for the White Sox than what team might want to acquire his talents.

"Yeah, I don't follow it too much," Danks said. "But like I said, that wasn't my concern to be attractive to any other team. I'm trying to get back and be effective for the White Sox.

"It's been a long road and you work so hard just to get back. You try to be effective, but you really don't know what you are going to have until you get out there and do it. If there's any interest, I don't want to say that's shocking, but surprising that it's so soon teams are interested in me other than the White Sox."

Konerko begins rehab stint Thursday at Double-A

PHILADELPHIA -- Paul Konerko moves into the Minor League rehab phase of his recovery for his balky back, starting Thursday with Double-A Birmingham.

The White Sox captain plans to play from Thursday through Sunday with the Barons, testing the lower back strain that put him on the disabled list July 3, while also getting some at-bats. Konerko hopes to get in the field at first base as well.

"We've passed all the tests and all the work here and last week gave it time just to rest," said Konerko before Sunday's first-half finale. "That was the main thing and then this week kicked in all the strengthening stuff and pieced our way back into it.

"I'd probably be leaving today or tomorrow, but the All-Star breaks in the Minor Leagues as well throw off that plan. We definitely want to play days in a row and see how it responds and also for the baseball side of it, to get some at-bats, to see some pitches because I've been out for a while now."

Konerko originally missed six games because of the back soreness and then returned for one game against Baltimore on July 2. The captain couldn't make it through that contest at full strength and was then inactive until this past Monday. He's gradually increased his workload every day, moving to flips in Detroit and then taking batting practice Saturday in Philadelphia.

By Konerko's estimation, he's done everything possible as far as recovery and it's time to get back on the field. So the All-Star break serves as the start of his return, as opposed to time off.

"I don't really see the All-Star break as a break for me because I haven't been doing anything," Konerko said. "I've been doing the work and stuff, but I've had my All-Star break for the last two weeks or whatever it has been.

"Even the week before that, I played one game. Obviously if we could go back in time, we would have done this right from the get-go and then took the time the first day I came in. But we had that week where I was off and felt like it was 90 percent and got back out there that one game against the Orioles, and it just reset all the way back to square one and then we decided to take this long chunk of time to get it right.

"Hindsight is 20/20," Konerko said. "I've had my rest. I want to play."

This rehab assignment means Konerko will miss next weekend's Atlanta series in Chicago and the return of Braves hitting coach Greg Walker, holding the same role he held with the White Sox.

Beckham out of lineup with left thigh bruise

PHILADELPHIA -- After suffering a left thigh bruise in the 12th inning of Saturday's second game, White Sox second baseman Gordon Beckham was out of Sunday's starting lineup.

"It's just a bruise, it's just a deep one," said Ventura of Beckham. "I highly doubt he would get in there today. You never know into the game or something like that, but as of right now he really doesn't have a chance of playing."

Ventura also wanted to stay away from reliever Ramon Troncoso in Sunday's first-half finale after the righty pitched in both ends of Saturday's doubleheader, but added that starting pitcher Dylan Axelrod was available out of the bullpen. Beckham will have time to recover during the four days off for the All-Star break.

"Breaks are good," White Sox first baseman Adam Dunn said. "I don't care if you are 50 games up or 50 games back. There's a few things that people circle during the year on their calendars: Opening Day and All-Star break are among the top two."

Phegley injures finger on foul; X-rays negative

PHILADELPHIA -- White Sox catcher Josh Phegley exited Sunday's 4-3 loss to the Phillies in 10 innings after taking a foul ball off of his right index finger during a Kevin Frandsen at-bat in the bottom of the ninth.

Phegley shook his hand loose after contact and briefly walked toward pitcher Nate Jones in an attempt to let the pain subside. But Phegley was walking off the field as White Sox head athletic trainer Herm Schneider and manager Robin Ventura were walking on the field to check on him. Phegley, who delivered the game-tying hit with two outs in the ninth off closer Jonathan Papelbon, was replaced by Tyler Flowers.

"It kind of caught him on his pointer finger," Ventura said. "But it didn't look good. There's no question to taking him out."

"That ball got me pretty square right on the finger and hurt pretty good immediately," Phegley said. "I looked down and saw a bump that didn't look normal, so I thought maybe something was sticking out, which shouldn't have been sticking out."

X-rays taken at Citizens Bank Park were negative, according to Phegley, with his hope being that the soft tissue swelled up after contact. He plans to be back on the field when the White Sox resume play at home Friday against the Braves.

"It's unfortunate, but fortunate that I'll have four days off to take care of it," Phegley said.

Draft talent should assist Sox in rebuilding process

PHILADELPHIA -- For at least a few weeks or months after the June First-Year Player Draft, White Sox director of amateur scouting Doug Laumann and his staff look like very astute baseball individuals.

"You're always optimistic the first month after the Draft," Laumann told MLB.com during a recent interview.

"We'll be pretty stupid again pretty soon," added Laumann with a laugh. "Now we can act like we are smart for a few weeks."

The truth of the matter is that with Tim Anderson (first), Tyler Danish (second) and Jacob May (third), the White Sox picked up three of Laumann's primary targets after months of extensive scouting. These three White Sox newcomers also will be essential to the team's rebuilding or reshaping, much like Trayce Thompson, Courtney Hawkins and Erik Johnson before them, to name just a few.

So far, so solid for some of these '13 Draft class members.

Anderson has a .303 average with eight stolen bases at Class A Kannapolis, while Danish has a 2.00 ERA with nine strikeouts in nine innings. May is struggling with four hits in 37 at-bats for Kannapolis, but already was promoted from Great Falls, where he hit .378 with seven RBIs in 45 at-bats.

Not everything is perfect, with Anderson having made 12 errors at shortstop and outfielder Courtney Hawkins, the team's top pick from 2012, having struck out 102 times in 203 at-bats, despite knocking out 15 homers. But it's all part of the learning process.

After all, Derek Jeter made 56 errors at shortstop during his first full Minor League season.

"As a scouting director and just anybody that is involved with these kids, you want them to get to the big leagues as quick as you can," Laumann said. "You love to see them jump levels and progress like want them to. You have to trust our guys in player development and [assistant general manager] Buddy [Bell], who is very good at reading where guys can handle, not just physically but mentally."

Third to first

• Ventura is not set yet in regard to his rotation to start the second half, aside from Jose Quintana not getting the call Friday and getting pushed back for an extended rest. The rotation will depend on how much Chris Sale throws in Tuesday's All-Star Game and Jake Peavy's effort during his Sunday rehab start for Double-A Birmingham.

"He could be back in the mix," said Ventura of Peavy. "But I'm not going to worry about that today."

* Ventura remains unsure of his AL coaching role for Tuesday's All-Star Game, adding that coaching third remains a possibility.

"It's not like I'm afraid to do it," Ventura said. "But we'll see when I get there and see what happens."

* Dunn gave props to Danks, who started Game 1 on Saturday against the Phillies, for making it into the seventh amidst the intense heat and humidity.

"I don't know how Johnny got through the first one," Dunn said. "I'm sure I've played in warmer, but I mean that was as bad as it gets."

• The White Sox finished 3-for-26 with runners in scoring position over Saturday's doubleheader split.

Scott Merkin is a reporter for MLB.com. Read his blog, Merk's Works, and follow him on Twitter @scottmerkin. This story was not subject to the approval of Major League Baseball or its clubs.