Muller has fallen behind Philippe Coutinho in the pecking order at the Bundesliga side and has been benched for their last five games.
Coach Niko Kovac all but confirmed the forward was no longer a starter stating: "When there's need, he'll get his minutes."
Bild believe the German wants out of Bayern as soon as possible which could see him leave in the January transfer window.
And Muller was a target of Liverpool in 2017, according to Bild journalist Christian Falk, with Klopp reportedly asking Bayern about the availability of the striker.
Falk also said Manchester United and Arsenal had shown an interest in the former German international with Louis Van Gaal prepared to pay up to £100million for his signature but a deal was unsuccessful.