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8/4/2014 9:13 P.M. ET

X-rays negative after Avisail hit by pitch in rehab

CHICAGO -- X-rays taken of Avisail Garcia's left arm were negative after he was hit by a pitch during a rehab assignment on Sunday, manager Robin Ventura said on Monday.

The versatile outfielder had a bruised left triceps but should be available for Triple-A Charlotte's next game, on Tuesday against Gwinnett.

Garcia, thought to be lost for the season after sustaining a torn labrum and avulsion fracture in his left shoulder on April 9, has five singles in 10 at-bats for Charlotte. He began his rehab assignment on Tuesday.

"Avi's doing good," Ventura said.

Ventura also said that pitcher Zach Putnam should be available to come off the 15-day disabled list on Friday, the soonest he's eligible.

"He's on track right now," Ventura said. "He's throwing tomorrow in Charlotte. He'll get an inning in there and see what he feels like."

Abreu earns second AL Player of Month honor

CHICAGO -- On Monday, the record-setting Jose Abreu was named the American League Player and Rookie of the Month -- again.

Abreu has won the league rookie honors every month this season except May, when he went on the 15-day disabled list with an ankle injury.

He took both honors in April. This second sweep makes him the first rookie in Major League history to win the Player of the Month award twice in one season, and the fourth to be named Rookie of the Month three times or more.

"I don't really like to talk about myself a lot, but I am surprised," Abreu said through interpreter and White Sox coach Lino Diaz. "I wasn't expecting to have all this success and definitely all these awards. But, you know, I am very thankful to God that happened. I just continue to go about my day the same way and continue to work on my routines."

In July, Abreu led the AL in batting average (.374), doubles (11), slugging percentage (.667), extra-base hits (17) and times on base (48).

He also put together a career-best 21-game hitting streak, the AL's longest this season. That was also the longest for the White Sox since Carlos Lee hit in 28 straight games in 2004.

"There is a limit of what guys are going to hit, statistically," said manager Robin Ventura. "But within the game of driving in runs and things like that, he's pretty good, and he's going to continue to get better at that in-game stuff."

Abreu drew more walks and had a higher on-base percentage in July than in any month prior, an indication that pitchers are working around him. He said that the biggest adjustment he's made since the start of the season has been patience at the plate.

"I really don't know the adjustments that [pitchers] made on me, I just know that I concentrate on myself," Abreu said. "I concentrate on my strength when I go there. I'm sure they're making adjustments and things like that, but I try to stay with what I do good."

Added Ventura: "He hasn't had too many at-bats of going after stuff out of the zone. Early he was swinging pretty good, and then he went through a period of trying to do too much, hitting too many homers and swinging at a lot of pitches. If you look at his at-bats over the last month, he's been pretty spot on."

Cleto called up from Charlotte

CHICAGO -- The White Sox on Monday purchased the contract of pitcher Maikel Cleto from Triple-A Charlotte, and in a corresponding move, sent Taylor Thompson to Triple-A.

In 22 games with Charlotte, Cleto went 3-0 with a 5.91 ERA, 50 strikeouts, 15 walks and three saves. He will provide a fresh arm to a struggling White Sox bullpen.

"He's been throwing great, and after [the relief corps allowed 15 runs on Sunday], you need a bullpen arm, and he's been the best guy down there," manager Robin Ventura said. "They said by far that he's been throwing it the best."

Cleto was claimed off waivers from the Royals in February and made the Opening Day roster, but he was optioned on May 12 to Charlotte, where he's remained since. He tossed 14 innings over 13 games, with a 5.14 ERA, before being sent down.

"We saw some pretty good stuff early in Spring Training," Ventura said. "The velocity and the power he has, he got to a point where the location wasn't there, but right now they say he's throwing great."

Third to first

• White Sox starters entered Monday with a 3.42 ERA in the last 36 games, the third lowest in the AL.

• Abreu is 5-for-13 in three games against the Rangers, with a homer, two doubles and three RBIs.

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