Klinsmann's fate was sealed after a meeting with club chairman Karl-Heinz Rummenigge, general manager UliHoeness and director Karl Hopfner on Monday morning.
First reported by Bild, Germany's mass-circulation tabloid, it momentarily displaced the negative headlines surrounding the club's president, former World Cup-winning forward UliHoeness.
Elsewhere, Bayern Munich striker Luca Toni looks set to depart the Allianz Arena in the near future after president UliHoeness confirmed he can leave the German Budesliga club.
Bosnia's Dzeko and Brazil's Grafite have scored 54 goals between them this season to break the previous record set by Bayern Munich's Gerd Muller and UliHoeness in the 1970s.