Koji Uehara allowed a hit but recorded all three outs via strikeout to earn the save against the Rays on Sunday.
Nick Cafardo of the Boston Globe reports that Koji Uehara is "in great demand," but the Red Sox "would like to hold on to him."
Koji Uehara racked up his 19th save of the season on Friday, working a scoreless ninth inning to protect a one-run lead against the Royals.
Koji Uehara will replace Masahiro Tanaka on the American League roster for the All-Star game.
FOX Sports' Ken Rosenthal reports that the Dodgers would be interested in a handful of Red Sox relievers should they be made available.
Koji Uehara admitted after Tuesday's game that the cause of his recent struggles might be related to "a little bit of fatigue."
Koji Uehara took his second loss of the season, allowing a run in the ninth inning in Tuesday's defeat at the hands of the Cubs.
Koji Uehara worked a perfect ninth inning against the Yankees on Sunday, preserving a three-run lead and earning his 18th save of the season.
Koji Uehara suffered his first blown save of the season on Sunday, allowing two runs in the ninth inning of an extra-innings win over the A's.
Koji Uehara allowed his third solo homer and his third run of the season on Wednesday, but he ended up with the win against the Twins.
Koji Uehara picked up his 14th save of the season, working a scoreless ninth inning in Thursday's win over the Indians.
Koji Uehara struck out two in a scoreless ninth inning to earn his 13th save against the Orioles on Tuesday.
Koji Uehara tossed a perfect ninth inning to pick up his 11th save of the season in Tuesday's win over the Braves.
Koji Uehara tossed a scoreless ninth inning Monday against the Braves for his 10th save of the season.