Putnam's last appearance came Monday night at Fenway Park, when he walked the bases loaded with nobody out in the ninth inning of a tied game. Zach Duke and the White Sox were able to escape that jam unscathed and went on to claim an extra-innings victory over the Red Sox.
Over 25 appearances, Putnam posted a 2.30 ERA with 30 strikeouts in 27 1/3 innings. Putnam features a 2.82 ERA in 123 career games with the White Sox, including six saves, with 140 strikeouts over 130 2/3 innings.
"Still parceling through the options," Hahn said. "At this point, we don't have a specific timeframe for him."
• Austin Jackson, who had surgery to repair a medial meniscus tear in his left knee, is on crutches for two weeks and then will have a follow-up MRI at the four-week mark.
"After that follow-up MRI, we'll have a little better feeling for a timeline for a potential return," Hahn said.
• Justin Morneau, who joined the White Sox via a one-year, $1 million deal with incentives, continues to work his way back from offseason surgery to repair the primary flexor in his left elbow.
"We are probably not too far away from announcing a rehab assignment at some point, and then we will have a little better feel for a precise return date," Hahn said. "We are still looking the other side of the All-Star break, but perhaps not too far thereafter."
Scott Merkin has covered the White Sox for MLB.com since 2003. Read his blog, Merk's Works, follow him on Twitter @scottmerkin, on Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.