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5/29/2014 1:07 A.M. ET

Abreu targeting return to lineup Monday in LA

CHICAGO -- A Minor League rehab assignment might not be needed for Jose Abreu before he is scheduled to come off the disabled list Monday in Los Angeles.

"We're going over that right now," said White Sox manager Robin Ventura of the plan for Abreu, who has been on the disabled list since May 18 with inflammation in his left ankle. "You're trying to see if you can get him the work here so he wouldn't have to go out.

"As of right now, there's not a plan for him to go out. He would stay here. I think [White Sox head athletic trainer] Herm [Schneider] wants him here just to watch him, and we'll figure out if we can get somebody here to simulate something to make him do it here instead of having to go play in a game."

The plan for Abreu is to have him back every day at first base when he's healthy enough to return. Everything is subject to change, but the unofficial target date remains the series opener against the Dodgers.

"He still says it's feeling better every time he goes out there," Ventura said. "He's tried a couple of different braces to try to alleviate what was there and to make it feel better and have more stability and things like that. It's a work in progress of trying to find the right mix right now that is going to be the one he goes forward with and plays with."

Even without their galvanizing force in the middle of the lineup, the White Sox have posted a 6-4 record entering play Wednesday.

"Keep on keeping on," said White Sox hitting coach Todd Steverson, whose offense has averaged 3.8 runs per game without Abreu in the 10-game stretch. "Things happen through the course of the year, whether it be through injury or someone has to leave for a family issue. The game's not going to stop because you don't have your typical full lineup that you want to have. Somebody has a job to do.

"With Jose back it's a lot more potent and a bit more dangerous. But nobody is going to cry for us that he's out of the lineup. We are still here to do a job. I'm happy for the fact that we still come to compete every day."

Confidence big part of Beckham's resurgence

CHICAGO -- As soon as Jose Abreu started to consistently pulverize baseballs upon joining the White Sox, the search for established player comps began.

Didn't Abreu's stance look a little like Albert Pujols? Could he find the same sort of yearly run production as Pujols?

Gordon Beckham, for one, would not bite on that particular topic.

"Based on past experiences of my own, I'm going to say, 'You know what, we'll just wait and see,'" said Beckham. "But he's very good, he's very humble."

Beckham burst on to the Major League scene in 2009, after being selected eighth in the 2008 First-Year Player Draft. He started in a 2-for-28 slide, but went on to earn two separate Rookie of the Year honors as voted on by his peers.

And then those pesky comparisons started, with many people describing Beckham as the next Michael Young. The hype followed, with talk of Beckham morphing from a top rookie into a perennial Most Valuable Player candidate, and the struggles Beckham faced off and on over his next four years became that much more heightened.

"I tried a little too hard. I tried to do a little too much," Beckham said. "Now, I feel good. I feel confident in what I'm doing. I've got a good feel for what I'm trying to do and hitting some balls hard. That's most important."

Entering Wednesday, Beckham was hitting .394 during his eight-game hitting streak and was hitting .361 in his last 20 games. He also had 13 hits in 28 at-bats against left-handed pitchers.

He's earning $4.175 million in '14, with one more year of arbitration in '15. Micah Johnson, Carlos Sanchez and Marcus Semien provide lower cost and younger options at second behind Beckham, but this solid production, combined with one of the AL's best gloves at second, makes Beckham an attractive option in his own right.

Whatever decision eventually is made, Beckham has fully arrived at a place where he's comfortable in the work he's doing and the process being followed. He's comfortable being himself.

"He's at a comfort level he hasn't had the last couple of years of knowing who he is, and the confidence he has day to day is part of it," said White Sox manager Robin Ventura. "Mechanically, you have to do things right, but mentally, you have to go with that, too. He's just in a good spot."

Gillaspie gaining consistency at the plate

CHICAGO -- Conor Gillaspie hit 13 homers during his 2013 debut with the White Sox. He also finished with a .245 average and .305 on-base percentage, compared to his current .352 average and .394 on-base percentage. But White Sox hitting coach Todd Steverson doesn't think Gillaspie is necessarily sacrificing power for average.

"He hasn't sacrificed any power," Steverson said. "He has hit some balls as sharp as anybody in this league, but they are just on a line. They don't have that kind of elevation.

"And it [isn't] about the average with me. It's what's behind the balls in play. And that matters for him. They have been good. He's been getting his doubles. A lot of people will say he doesn't have any home runs or nothing. It doesn't mean he can't do it, but you want to be a hitter first."

The White Sox have liked Gillaspie's easy swing since they acquired him from the Giants in Spring Training of 2013. Steverson said that Gillaspie has a "knack for the barrel" and doesn't have a whole lot of moving parts to his swing.

"Kind of a 'see it and hit it' kind of guy," Gillaspie said.

That combination could add up to Gillaspie consistently challenging that .300 mark.

"He's got the ability to consistently put balls in play, which gives him the opportunity to have that possibility," Steverson said. "To be a .300 hitter, you need to put the ball in play and keep taking your walks and then have a lot of luck. In baseball there aren't a whole lot of .300 hitters in general."

Alexei admires Jeter's contributions to game

CHICAGO -- Alexei Ramirez's statistics are better than Derek Jeter's across the board through the first two months of the 2014 season. In fact, Ramirez has been the best shortstop in the American League during that time.

But Ramirez thoroughly understands the All-Star voting support received by Jeter, who is one of the game's biggest and most respected stars, playing in the final season of a two-decade career.

"You have to tip your hat to Derek Jeter. That's a guy we look after and it's a great model," said Ramirez through interpreter and White Sox manager of cultural development Lino Diaz. "I am very pleased to be right next to somebody like that."

In the first round of AL voting released Tuesday, Jeter's vote total sat at 602,525 and Ramirez's at 472,537. Ramirez would be honored to take part in Jeter's final All-Star appearance.

"I admire Derek Jeter as a person and as a player," Ramirez said. "He's a legend. He deserves this more than anything else for everything that he's done in all his career."

Third to first

Adam Dunn has been playing more games at first base than Paul Konerko during Abreu's absence because Konerko has dealt with occasional back stiffness.

"Sometimes that happens where he gets locked up," said White Sox manager Robin Ventura of Konerko's back. "Right now, it has worked out better to have Dunner over there where he's able to do it."

Dunn has made 14 starts at first, with Konerko making six.

Chris Sale was amused by the video of him lip-syncing and dancing to Call Me Maybe from Alex Rios' wedding in '12 that made its way to TMZ Sports. Sale enjoys karaoke, with his go-to song standing as Man in the Mirror.

"I thought he was great. I thought he was really good," said a smiling Ventura of Sale. "That needs to be a competition on our team. He seems like he likes to have fun. That's what I took away from that."

• Kyle Long, the Bears offensive lineman, threw out one of the ceremonial first pitches prior to Wednesday's game. Long was selected by the White Sox in the 23rd round of the 2008 First-Year Player Draft, but the left-handed hurler didn't sign.

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.