Odorizzi went 4-5 with a 2.47 ERA in 12 starts this season prior to going on the disabled list on June 9 with a left oblique strain.
Reliever Andrew Bellatti (right shoulder tendinitis) will pitch for Charlotte on Friday night. After that, it's likely he will be available for the Major League club.
"He's responding really well," Cash said.
Cash allowed that where Bellatti goes once he's ready depends "on where we're at" in the bullpen.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.