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3/9/2014 8:12 P.M. ET

No thought of Keppinger to DL

PHOENIX -- There are continued limitations defensively for Jeff Keppinger and his sore right shoulder. But that post-surgery soreness or tightness, which doesn't have him throwing at full strength from third to first, has not kept him completely out of the White Sox starting lineup.

Keppinger finished 0-for-3 with a RBI at designated hitter Sunday against the A's at Municipal Stadium and will DH again on Monday against the Brewers.

"His arm, it's been slower than you would think," said White Sox manager Robin Ventura of Keppinger's rehab. "But it continues to get better. Sometimes it takes a lot longer than you would like and right now it's a slow process. But he can hit, so I'm making sure he gets his at-bats."

After undergoing a debridement of his right shoulder Sept. 27 at Rush University Medical Center in Chicago, Keppinger was expected to recover in two to three months and be ready for Spring Training. But while his shoulder is not at full strength, it has not hampered his hitting, per Ventura.

Ventura has not entertained thoughts of Keppinger starting the season on the disabled list with plenty of time remaining for his shoulder to get in regular season shape.

"I remember having the same thing, a year where it took a long time to get the shoulder in shape," Ventura said. "Once he's there, you feel pretty good about it. Just the timing of hitting and things like that, you want to get him his at-bats."

Conor Gillaspie, one of the third base candidates, earned praise from Ventura on Saturday for his overall improvement shown during Spring Training. Ventura talked Sunday about liking the strides being made by Matt Davidson, a major part of the club's young core, who scould break camp with the team despite the talent heft at that spot.

"He's making some strides I think of just feeling more comfortable," said Ventura, focusing on Davidson's defense. "He's getting a little more confidence as he's over there that it just looks better. The preparation, pre-pitch routine is getting a little better and he's getting off the ball a little bit.

"When he hits it, it's going to go a long way. He's a big strong kid. We seem to have a lot of those guys so sometimes you don't notice it because we have a lot of big guys around, but he has some pop. He has pop the other way and he just needs time. He needs to be able to play."

Webb debuts after dealing with family loss

PHOENIX -- White Sox reliever Daniel Webb made his Cactus League debut by pitching a scoreless seventh inning during Sunday's 2-2 tie with Oakland.

This effort also marked the rookie's first appearance after missing one week to deal with a death in the family back home in Kentucky. Webb threw a bullpen session in front of pitching coach Don Cooper on Friday and was happy to get back into competition.

"It's tough but being back here keeps my mind off it," Webb said. "It's good to see everybody and I'm ready to keep going.

"I feel like I didn't miss out on much. I threw while I was at home. My arm feels good. It's like I never left."

Webb threw two sidelines while he was away from camp. He allowed two singles Sunday, but struck out John Jaso to strand runners at second and third.

"It felt good to be back out there, get another hitter in the box other than a teammate," said the White Sox closer candidate. "I missed my spot a couple of times, but everything feels good and I'm happy with it."

Ventura's focus on who's in camp, not rumors

PHOENIX -- As Spring Training has progressed and Cactus League games reach double-digits played, the trade rumors have started to pick up.

Dayan Viciedo and Alejandro De Aza, the current White Sox left field tandem, have received frequent mentions in those rumors, with radio station 670 The Score reporting that Viciedo has been the topic of talks with the Mariners. Viciedo told MLB.com recently that he doesn't concern himself with off-the-field matters he can't control, and Robin Ventura didn't sound like a manager waiting for general manager Rick Hahn to pull off another trade or two.

"Right now I'm looking at it from just what's here," Ventura said Sunday. "Something could come up and that changes, but I'm preparing with this group.

"If something happens, then you can roll with it and change and go from there. Right now it is what it is here and you have to get your roster together with these guys."

Viciedo and De Aza aren't necessarily being shopped, but as Hahn made clear since the start of the offseason, pretty much anyone is open for discussion coming off of last year's 99-loss effort. Those discussions might be a little tougher to be heard if the names of Chris Sale, Avisail Garcia, Jose Abreu or Jose Quintana are mentioned.

But Hahn and the White Sox are not looking for a quick fix in return and want to enhance the reshaping program already well underway.

Quintana feeling better after liner incident

PHOENIX -- White Sox left-hander Jose Quintana was moving around without much restriction, telling the media that he went through his throwing program Sunday after taking a Gerardo Parra line drive off of his left shin Saturday.

Quintana exited from that contest after two batters and was diagnosed with a bruise. He hopes to throw a bullpen session Monday, but it could be pushed back to Tuesday with a focus on making his next start Thursday against the Angels.

"I feel a little bit of pain, but it's normal for the first day. [Monday] it will be OK," Quintana said. "[White Sox head athletic trainer] Hermie [Schneider] said day by day. But I feel really good right now."

The White Sox certainly won't rush Quintana back into action during Spring Training until they know he's 100 percent healthy. Although he might be penciled in at something other than the rotation's No. 2 slot behind Chris Sale, he's one of the three main cogs in the rotation and counted on for over 200 innings and 30 starts.

Ventura would consider skipping Quintana on Thursday with another two weeks still left in Spring Training after that potential start.

Rienzo in play for bullpen spot

PHOENIX -- Andre Rienzo won't be part of the White Sox starting rotation at the season's outset, barring something unexpected. That fact doesn't necessarily mean he's headed to the Minors.

One spot appears to be left in the bullpen, with Daniel Webb, Jake Petricka and Maikel Cleto a few of the hurlers in play. If the White Sox decide to go with a long reliever, Rienzo jumps near the top of that list.

"You start looking at what he did [Saturday] and you can bounce around ideas of what you need and you know how he could fit," said manager Robin Ventura of Rienzo. "And that's with a lot of these guys that start getting down to the end of Spring Training. How you are going to make it work?"

Rienzo made 20 starts for Triple-A Charlotte last year and 10 for the White Sox. But it was his five-strikeout effort over three innings in relief of Jose Quintana on Saturday that led Ventura to term that effort the best he has seen the right-hander throw.

That praise brought a smile to Rienzo's face.

"[I'm] glad to see something good," said Rienzo with a laugh, adding that he has focused on keeping the ball down and trying to throw more strikes. "The only thing I have in my hands is throw the ball and do my job. It's Ventura and his staff, I don't know what they are going to do with me. But I will try doing my best every day, every time."

Third to first

• Ventura pointed out Sunday that there's more to right fielder Avisail Garcia than his big frame.

"You don't notice how fast he is just running the bases," Ventura said. "He's a big kid and can play center field.

"At-bat wise, he's not just swinging as hard as he can kind of guy. He can hit for average and there's not that many people who are that big and can control that and still be able to have the kind of power he has. He's a unique individual."

Adam Dunn will get a chance to play left field before Spring Training comes to a close. Ventura said more flexibility will come in using players when the roster is reduced. Dunn had his second straight day off with Keppinger getting at-bats at DH, with Ventura adding that Paul Konerko will get two straight off as well.

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.