Nathan became a free agent on Friday when he declined a $9.5 million contract option for next season.
He will be the most sought-after closer on the free agent market and could earn at least the qualifying offer amount per year. If the Rangers do not make the offer, they will not receive a draft pick as compensation for losing Nathan.
The veteran closer, who turns 39 later this month, had a stellar 2013 season, posting a 6-2 record with 43 saves and a 1.39 ERA in 65 innings. He now ranks 10th on baseball's career saves list with 341.
In two seasons with the Rangers, Nathan compiled 80 saves and a 2.09 ERA in 126 innings. Texas took a gamble in signing him after he struggled with the Minnesota Twins in 2011 while coming back from reconstructive elbow surgery.
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Boston Red Sox second baseman Dustin Pedroia expects to have surgery on his left thumb.
Pedroia played through a torn ulnar collateral ligament for much of the season. He told Boston radio station WEEI that he will address the injury "probably in the next couple of weeks."
He will make a final decision on the surgery after having an MRI.
Pedroia injured his thumb while diving into first base on Opening Day, but played 160 regular season games and 16 playoff games.
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The Tampa Bay Rays picked up 2014 club options for second baseman/outfielder Ben Zobrist and shortstop Yunel Escobar on Saturday.
Zobrist who played five different positions this season, will make $7 million next year.
The club also has a $7.5 million option for the 32-year-old in 2015.
Escobar, 31, will earn $5 million next season. The club also holds a $5 million option for Escobar in 2015.
The Rays also have option decisions to make on outfielder David DeJesus ($6.5 million) and right-hander Juan Carlos Oviedo ($2 million).
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