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7/28/2013 12:44 P.M. ET

Rangers have discussed dealing closer Nathan

CLEVELAND -- The Rangers, with their offense in a downward spiral, have "checked on every bat with a pulse," according to Major League sources, and are not having any success. One source said the only real bat available is Phillies third baseman Michael Young, and a reunion with the Rangers is not likely to happen.

The Rangers are also not getting anywhere in their pursuit of White Sox outfielder Alex Rios. The Rangers have had multiple discussions with Chicago, but right now the asking price is too high and the chances of a trade appear dim.

The Rangers, trying to figure out some way to shake up their team, have even discussed the possibility of trading closer Joe Nathan. With a number of teams looking for bullpen help, Nathan could be the Rangers' best trading chip before Wednesday's non-waiver Trade Deadline and get the most for them in return.

"I've never worried about this stuff and I'm not going to start now," Nathan said. "I'm going to play and help this team win. My thought process is battling with this team and helping us get to postseason again. Obviously I've enjoyed myself here and enjoy my teammates. I love everything about this organization and the way they treat their players. I'm assuming I'll be here the rest of the year."

Nathan went into Sunday's game against the Indians with 32 saves in 34 opportunities. He had a 1.73 ERA and opponents were hitting .167 off him. But the Rangers also have Joakim Soria, who was an All-Star closer for the Royals and had 160 saves in 2007-11 before missing all of last season because of Tommy John surgery. Going into Sunday, Soria had not allowed a run in six appearances since being activated off the disabled list.

Nathan is in the second year of a two-year, $14.75 million contract. The Rangers also have an option for next season at $9 million with a $750,00 buyout. Nathan can void the option and automatically become a free agent if he has 55 games finished this season. He has 39.

Soria signed a two-year contract with the Rangers last season and could move into the closer's role if Nathan leaves. Neftali Feliz, who had Tommy John surgery a year ago, could be another option. He has been working out all season in Surprise, Ariz., and has been throwing live batting practice. He could go on a rehabilitation assignment and start pitching in the Minor Leagues in the next 10 days.

"I've put myself in a position where it gives them a decision to make," Nathan said. "I know it can be mutual, and there's a decision I have to make. I'd like to stay here. I think I've put myself in a position where things will be OK either way."

Nathan has been the Rangers' best pitcher this year and their bullpen has been their biggest strength. Rangers relievers went into Sunday with a 1.17 ERA in their last 17 games, lowering their overall ERA to 2.95. That's the lowest in the American League and the second lowest in club history. Rangers relievers had a 2.91 ERA in the strike-shortened season of 1981.

Harrison ready for Minors rehab assignment

CLEVELAND -- Rangers pitcher Matt Harrison is ready to pitch in Minor League games. Harrison said he expects to begin a rehabilitation assignment on Wednesday and pitch two innings for either Triple-A Round Rock or Double-A Frisco. Harrison is scheduled to throw in the bullpen on Monday.

Harrison was the Rangers' Opening Day starter but underwent surgery to repair a herniated disc in his lower back on April 23. He had a second operation on May 2. Harrison will likely need four or five starts in the Minors before he can be an option at the Major League level.

Worth noting

• Pitcher Michael Kirkman, who has been on the disabled list since June 7 while getting treatment for skin cancer, could be ready for a rehabilitation assignment in the first week of August. He has been working out in Arizona.

• Pitcher Nick Tepesch, who is on the disabled list with inflammation in his right elbow, remains limited in his throwing and has not yet started throwing off a mound. He has been on the disabled list since July 6.

• Adrian Beltre went 19 games without striking out before doing so in the first inning on Saturday night. He fell two short of the club record held by Frank Catalanotto.

T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.