Aside from moving Scott Carroll from long relief back to the rotation, there don't seem to be many options for a potential Rienzo replacement.
"That would be the option is to flip-flop," Ventura said. "Right now, I don't know if you can necessarily just put Andre out in the bullpen. The way Scotty throws strikes, you like if you are going to bring a guy in out of the bullpen, he's going to be able to do what Scotty has done."
Carroll has a 1-3 record with a 6.15 ERA in five starts this season. He features a 1.83 ERA over 19 2/3 innings as a reliever, benefiting from adding the cutter to his repertoire.
"Adding the cutter has been a big pitch. It has helped a lot with lefties," Carroll said of the pitch he incorporated after his May 19 start in Kansas City. "We came back home and started playing catch with it and it has been feeling good and it has been a big pitch for me."
"Just because you try to teach a guy a cutter, it doesn't mean he's going to get it and be able to use it," Ventura said. "To his credit, he's able to mix it in and it's happened pretty quick for him."
Eric Surkamp, who is on the White Sox 40-man roster, could be another option. He has a 3.98 ERA over his last 10 starts for Triple-A Charlotte, with 67 strikeouts in 54 1/3 innings. He would also give the White Sox four left-handed starters.
Scott Merkin is a reporter for MLB.com. Read his blog, Merk's Works, and follow him on Twitter @scottmerkin. This story was not subject to the approval of Major League Baseball or its clubs.