Sources: Red Sox seek bullpen help

The Red Sox, continuing their search for bullpen help, are maintaining contact with the White Sox and Brewers about possible trades, according to major league sources.

The White Sox, sources say, are actively shopping two potential free agents, lefty Matt Thornton and righty Matt Lindstrom. The team, however, is unlikely to trade its closer, right-hander Addison Reed, who is under club control through 2017.

Righty Jesse Crain, a potential free agent who figured to be in the highest demand of any White Sox reliever, is on the disabled list with shoulder soreness.

The Brewers, like the White Sox, are motivated to trade some of their bullpen pieces. The Red Sox have been scouting the Brewers, sources say, and their possible targets include right-hander Francisco Rodriguez and lefty Mike Gonzalez.

Rodriguez, 31, is 9-for-9 in save opportunities and owed less than $1 million for the rest of the season. Gonzalez, like the White Sox’s Thornton, would add to the Red Sox’s depth from the left side.

Craig Breslow is the Red Sox’s only left-handed reliever. Andrew Miller is out for the season with a left foot injury, and Franklin Morales remains on the DL recovering from a strained left pectoral.

The Red Sox also have checked in with the Giants about possible trades for relievers, but the Giants are uncertain of their direction, sources say. Boston also could jump on other bullpen arms as they become available; the Rockies, for example, could trade Rafael Betancourt if they fall out of contention in the NL West.