Nagelsmann was in charge when Bayern lost 2-1 at Bayer 04 Leverkusen on Sunday and Borussia Dortmund moved top of the Bundesliga.
Nagelsmann took charge in 2021 and led Bayern to their 10th German title in a row last season.
They play Manchester City next month in the Champions League quarter-finals.
Media outlets are reporting that former Chelsea and Dortmund manager Thomas Tuchel (49) is set to be appointed as Nagelsmann's successor.
