Baker admits that off-days on consecutive Thursdays will influence a shakeup, but he was not ready to commit to something Friday.
"Why you got to ask me that every day? I'll let you all know," said Baker, who noted Cingrani did not travel with the team to Milwaukee. "We've got three or four options. It depends on where we are, it depends on the standings, it depends on a lot of things. We've got options. The off-days give us options."
If Cingrani can't make his scheduled Tuesday start, one possibility would be Cueto, who has been on the DL since June 29 with a strained right lat muscle. Cingrani was Cueto's replacement in the rotation, but the left-hander exited his Tuesday start after just 1 2/3 innings due to back spasms.
Cueto threw a successful bullpen session on Wednesday, throwing 60 pitches from the windup and the stretch.
The Reds have not announced their Monday and Tuesday starters yet for the first two games in Houston, and Baker said the team may not know the exact plan to finish the season until it is in Pittsburgh a week from Friday.
"Don't ask me this every day," Baker said. "Ask me this probably next week. In Pittsburgh, we'll have a pretty good idea."
Kevin Massoth is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.