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7/7/2014 7:41 P.M. ET

Avisail making progress toward '14 return

BOSTON -- Avisail Garcia took batting practice on the field Monday for the first time in his extended rehab program from the torn labrum and avulsion fracture in his left shoulder sustained while diving for a fly ball in right on April 9 at Colorado.

While White Sox general manager Rick Hahn won't change the original timeframe that had the powerful right fielder being sidelined for the season, he did present a glimmer of real hope that Garcia could play again this season.

"Is it possible he returns to Major League play this year? Yes, it is possible. However, we are still many steps in the rehabilitation away from that," Hahn said Monday at Fenway Park. "Ultimately, the decision about whether Avi plays at the big league level this year will be dictated primarily by his health and secondarily by what's best for his development.

"The club's performance, the club's won-loss record, the situation of the club later in the season once he has progressed to that level, will not be relevant in deciding whether or not he's going to play. It's going to be decided by his health and what's best for his development going forward.

"He has obviously done a tremendous job in his rehabilitation," Hahn said. "Our doctors feel very good 12 weeks post-op that physiologically the fracture and the repair have healed, so now it's just a matter of slowly progressing him back into baseball activities and see what timeline that leads to in terms of a potential return."

At the very least, Garcia looks more certain for playing winter baseball or even in the Arizona Fall League. Garcia told MLB.com at the end of May that he had not given up hope for coming back this season, and that hope might produce a September callup of sorts.

"Putting aside the physical issue, which we seem to be slowly getting to the other side of, which is obviously quite good, the biggest problem with Avi's injury is missing that development time at the big league level," Hahn said. "He's still a young kid. Getting him those repetitions at the big league level, those plate appearances are very important.

"So yes, there is, from a developmental standpoint, a benefit to getting late decent ABs if, again, his health and prudence dictates that makes sense. We do see benefit in that."

Hahn quipped that the White Sox will have to teach Garcia the outfield slide when going for fly balls, avoiding the headfirst attempt that cost him much of the '14 season. While any player with an injury is at a heightened risk of re-injury, Hahn said that risk for Garcia is no greater today than it will be five years from now.

Hahn not feeling urgency to make moves

BOSTON -- In the opening stages of this current White Sox reshaping process, the White Sox felt a need to move veterans Jake Peavy, Matt Thornton, Jesse Crain and Alex Rios before the 2013 non-waiver Trade Deadline to get younger, controllable talent to enhance the product.

That same urgency is not felt by general manager Rick Hahn as the present July 31 deadline approaches, despite names from Dayan Viciedo to John Danks to Gordon Beckham to even All-Star Alexei Ramirez being tossed around the rumor mill.

"We are at a different point," Hahn said. "There's certainly no urgency to do anything. I think most of the players I've read about online that are rumored to be out there are all under control beyond this season. There's no urgency to cash in an asset, so to speak, before it expires.

"Again, we are willing to make a deal at any point where it makes most sense for our long-term interests. Whether that happens in the next two weeks or it takes until the offseason or Spring Training next year, we are not going to force the issue."

Hahn added that pitching remains a priority but has always been a team priority even when the club seemed to have an abundance of top-notch arms.

"There's never really a spot where any of the 30 clubs feel like they have enough pitching," Hahn said.

Abreu's parents to attend All-Star Game

BOSTON -- Many stories have been told about Jose Abreu's deep connection to his mother, and of course how he missed both his mother and father while playing for the White Sox in Chicago. They were not in Cuba, but until two months ago, they also weren't in the United States.

Abreu's parents currently are living in Florida, but have watched him play in Chicago. They will get a chance to see their son perform on an even bigger stage at next Tuesday's All-Star Game at Target Field.

"There are no words to describe how I feel just to be able to have them be there for something that you work as hard as I have for this," said Abreu through interpreter and White Sox manager of cultural development Lino Diaz. "There are some times when I'm talking to them and I'm telling them about these things that they don't believe and sometimes I don't believe that it's happening. It is a great thing and we enjoy it."

Abreu and Alexei Ramirez became the eighth pair of Cuban teammates in Major League Baseball history to be selected to the All-Star Game and second for the White Sox. Minnie Minoso and Sandy Consuegra made the AL team in 1954. Abreu stands as the White Sox fifth rookie All-Star, joining Ron Kittle (1983), Carlos May (1969), Tommie Agee (1966) and Minoso (1951).

Gillaspie out of lineup with sore right knee

BOSTON -- Conor Gillaspie had noticeably better movement getting around the visitors' clubhouse at Fenway Park on Monday in comparison to when he took a Dominic Leone pitch off of his right knee in Sunday's 1-0 victory over the Mariners. Gillaspie left that game and was out of Monday's lineup.

"He's moving a little better," said White Sox manager Robin Ventura. "But he's sore, and we just felt it was better to give him today and make sure he's able to get out there and move around and dive and do all that stuff. He's pretty sore today."

Gillaspie had X-rays on the knee that showed no break. He has some swelling in the joint on a pitch that ricocheted off his knee and bounced high into the air, sounding as bad as it looked.

"It's not pleasant," Ventura said. "Hopefully, by tomorrow he should be fine. By the miracle of [White Sox head athletic trainer] Herm [Schneider], he might be able to pinch-hit tonight. He probably could. I don't know if he'd stay in there, but he might be able to pinch-hit."

Third to first

• Hahn had nothing to update in regard to negotiations between the White Sox and Carlos Rodon, their top pick in the 2014 First-Year Player Draft and No. 3 overall selection. The White Sox and Rodon's camp have kept the ongoing negotiations almost completely out of the media.

July 18 stands as the deadline to sign the left-handed hurler. If Rodon does not sign and returns to North Carolina State, the White Sox will get the fourth pick in 2015 along with their own. Hahn also wouldn't speculate as to whether the extended negotiations have cost Rodon a chance to pitch for the White Sox this season.

"I don't think it's really fair to plot something out until he's on campus and in uniform and working with our guys and we can see exactly where he is," said Hahn. "Obviously, he hasn't thrown a pitch since May 16, so time has passed since then and ultimately, should we get him in here, we have to start the process of building him back up before assessing any timeline."

• Since June 23, the White Sox have the best AL starters' ERA at 2.79.

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.