Greene (hip) threw a side session Tuesday as part of a core stability program, MLB.com reports.
Cincinnati manager David Bell said Greene has one more level to achieve in the program. Once the right-hander finishes that, Greene will throw a live batting practice session then head out on a rehab assignment. "It could all happen really fast," Bell said. "Any day, it's going to happen." Greene will continue with the program at the team's complex in Goodyear (Ariz.) before a rehab assignment at Triple-A Louisville or High-A Dayton.