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7/25/2013 3:45 P.M. ET

Claiborne holds special Arlington memories

ARLINGTON -- Preston Claiborne can recall sitting in the green seats along the third-base line at Rangers Ballpark, watching his hometown Rangers try to outplay the visiting Yankees and marveling at how big a stadium can seem when you're 7 or 8 years old.

Claiborne also vividly remembers what his father, Michael, told him that day: The Yankees organization represented class, dignity and playing the game the right way. Claiborne absorbed the message.

"It was a Yankees-Rangers game, and my dad was telling me to play like the boys in pinstripes," Claiborne said. "Obviously, as a Dallas native, we were happy when the Rangers won and we cheered when we got a chance to go to the games, but I always grew up loving the Yanks and the way they went about their business."

Claiborne was born in Dallas and attended high school in nearby Carrollton, Texas, before heading to Tulane. The right-handed reliever said that he had been thrilled when the Yankees called his name in the 17th round of the 2010 First-Year Player Draft.

"When I was young, it was in the heyday of them winning their championships -- that's what I wanted," Claiborne said. "I wanted to be a part of these legendary teams, and now I have the opportunity to do that."

Claiborne's father passed away during the hurler's sophomore year at Tulane, but the memory of that first game made it a significant moment when the Yankees called upon Claiborne on Tuesday against the Rangers.

His spikes digging into the same playing field he once paid admission to see, Claiborne pitched 1 1/3 scoreless innings in the Yankees' 5-4 win.

"It was special, being that my first game was here with my father," Claiborne said. "But when I'm out there, I'm not thinking about special moments or anything, and I know he wouldn't want me to, either. When the skipper hands me that ball, it's business time and I've got to go to work."

No pain for Jeter after first baserunning drill

ARLINGTON -- Derek Jeter ran the bases without incident on Thursday at Rangers Ballpark, showing no ill effects from his right quadriceps strain. Could a return to the Yankees' lineup be on deck?

Jeter has said that he hopes to be activated for Saturday's game against the Rays at Yankee Stadium.

"I don't feel it, so that's good," Jeter said. "Whatever they tell me, man. I think I can play today. I do what I'm told. I'll go inside and see what we have tomorrow."

Jeter ran several times on the basepaths, including from first base to third base and second base to home plate, under the watch of conditioning coach Dana Cavalea.

The Yankees' captain also took a round of batting practice, slicing line drives to the outfield, and he went through fielding practice at shortstop with infield coach Mick Kelleher.

"I feel good," Jeter said. "That's the only thing I can say; I feel good. I don't feel [pain in] my leg, which is good. Now, it's up to them. I don't know what they have planned."

Yankees manager Joe Girardi said he would still be surprised if Jeter is playing on Saturday, but he wouldn't rule it out.

"The one thing that you can't do is say, 'Well, he's definitely going to be there,' and then when he's not there, all these flags go up," Girardi said. "Let's see how today goes, then we'll see how tomorrow goes, then we'll go from there."

After a three-game homestand with the Rays beginning on Friday, the Yankees will head for the West Coast to play the Dodgers and Padres. Jeter said that he did not believe playing in National League cities would be an issue.

"No problem -- we have a lot of days off coming up," Jeter said. "We have this weekend, then a day off [Monday], then two games and we have a day off. Then six games and another day off. We have a lot of days off. I'm not concerned with that. I don't make the lineup, but I'm not worried about that."

Wetteland helps Rangers pay tribute to Mo

ARLINGTON -- The Rangers honored Yankees closer Mariano Rivera on Thursday with a few Texas-themed gifts before his final regular-season game at Rangers Ballpark.

The Majors' all-time saves leader received a cowboy hat as well as a custom pair of boots with his name and the Yankees logo stitched on the front. The Texas Rangers Baseball Foundation also presented Rivera with a $5,000 check for his foundation. Rangers CEO Nolan Ryan, closer Joe Nathan and former Rangers and Yankees closer John Wetteland took part in the ceremony.

"When you look back, from where he started and the process of how Mariano Rivera -- not a scared kid, but a wide-eyed kid -- becomes arguably, then far and away, the greatest closer that ever lived, you can kind of see it now," said Wetteland, who was the Yankees' closer during the 1996 World Series, with Rivera setting him up.

"The thing that blows my mind is how the body holds up. We all take care of our bodies; energy in and energy out. We all tend to those things, but there are a special few that are blessed with the ability to keep going. That's something that's very special that I can't explain."

Rangers manager Ron Washington pointed to Rivera's ability to locate his cutter as the reason for the closer's success. While hitters may know the pitch is coming, Washington said Rivera has hardly hurt himself with a lack of command.

"He set a standard that I don't think anyone will ever [match]," Washington said. "He's automatic, and any other other adjective that you can find to describe him in a bright, bright, bright, bright light, that's what you do. Class act."

Bombers bits

• Yankees outfielder Brett Gardner was not in the lineup on Thursday, and Girardi said that was just to give the speedster a break after he appeared to tire near the end of the first half.

"I felt like today was a good day," Girardi said. "He probably won't get a day off for a while after that because the schedule is really conducive to playing every day. I'm just trying to be smart about it."

• Rutgers head football coach Kyle Flood will throw out the ceremonial first pitch prior to Friday's game at Yankee Stadium.

• On this date in 1998, the Yankees dedicated a Monument Park plaque in honor of Mel Allen, the "Voice of the Yankees" from 1939-64.

Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. Master Tesfatsion is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.