The German giants thrashed Barcelona 8-2 in the quarter-finals, who finish the season without winning any major trophies.
Club president Bartomeu met with director of football Eric Abidal and fellow chief Ramon Planes late on Sunday night and confirmed to reporters afterwards Setien was ‘out’.
An official announcement is expected on Monday, with Barcelona scheduling a press conference in the afternoon.
Setien was only appointed in January to replace Ernesto Valverde, but fared little better than his sacked predecessor as Real Madrid beat Barcelona to the La Liga title.
Netherlands coach Ronald Koeman, former Tottenham boss Mauricio Pochettino and Barcelona legend Xavi are all in the frame to replace Setien.
Former Everton boss Koeman is thought to be the frontrunner as a former Barcelona player and a manager with plenty of experience.
The news of Setien’s dismissal comes hot on the heels of reports Messi is ready to call time on his incredible career at Barcelona.
The club have been forced to deny Messi has told the board he wants to leave unless there is significant changes made.
While Messi has demanded action, Barcelona have put almost the entirety of their squad up for sale following the defeat to Bayern.
The presidential elections are scheduled in 2021, but may be held this year amid calls for Bartomeu to step down.