Greene (shoulder) is expected to begin a rehab assignment Thursday with Triple-A Louisville, Byron Kerr of MLB.com reports.
Greene's strained right shoulder responded well to him facing hitters in live batting practice Saturday, so the rookie looks like he'll be ready to move on to the final phase of his recovery program. He's expected to make two rehab appearances in the minors, as Reds manager David Bell said Sunday that if all goes well, Greene will likely return from the 15-day injured list to rejoin the big-league rotation Sept. 11 in Milwaukee or Sept. 12 at home versus the Pirates.