Greene (shoulder) will make his next rehab start Tuesday with Triple-A Louisville, Bobby Nightengale of The Cincinnati Enquirer reports.
The 23-year-old recovered well after tossing two scoreless frames in his first rehab outing Thursday, and he'll remain on a five-day schedule for his next start with Louisville. According to Mark Sheldon of MLB.com, Greene threw 27 pitches in Thursday's game plus eight more pitches in the bullpen, and he should continue building up his workload Tuesday.