Despite winning six trophies during his 17 months in charge, Flick's future at the Allianz Arena is uncertain following a disagreement with Hasan Salihamidzic.
The 56-year-old is among the contenders to replace Joachim Low as Germany head coach after this summer's rescheduled Euro 2020 tournament.
Should Flick step down, 90min claims that Bayern will turn their focus to Liverpool manager Klopp.
The former Borussia Dortmund boss is under contract at Anfield until 2024, but the report suggests that the Bavarian giants are ready to test his resolve.
It is suggested that Klopp may be growing frustrated at Liverpool and would be open to the opportunity to manage Germany's biggest club.
Klopp was previously interviewed for the Bayern job in 2008, but it was instead given to Jurgen Klinsmann. body check tags ::