BILD says the Blues could be set for a sensational move for Neuer this summer after appearing to finally lose patience with Kepa Arrizabalaga.
World record signing Kepa has come under pressure this season after recently losing his place to 38-year-old deputy Willy Caballero.
The Spaniard was dropped after a series of error-strewn performances in January, but regained his place shortly before the season was curtailed by coronavirus.
And Neuer, despite his advancing years, is seen as the ideal replacement by Frank Lampard.
Neuer, 34, is set to enter the final year of his contract at the Allianz Arena having failed to agree new terms.