The Reds set their rotation on Friday and Chapman isn't included. He came to camp with the possibility of becoming a starter, but will stay in the bullpen for the NL Central champions.
Chapman had 38 saves in 43 chances last season. The hard-throwing lefty became the closer on May 20 and later converted a team-record 27 consecutive saves.
Cueto will be the opening day starter for the second year in a row. He won a career-high 19 games last season.