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 according to German newspaper Bild, Neuer is seen as the ideal replacement by Frank Lampard.
Neuer is set to enter the final year of his contract at the Allianz Arena having failed to agree new terms. The 34-year-old is believed to want a significantly longer contract than Bayern, who he joined from Schalke nine years ago, are prepared to offer him.
Bayern have already signed Alexander Nubel from Schalke and see the 23-year-old as one the best young keepers in Germany.
Reports in Spain also indicate that they are preparing a world record £80m bid for Neuer’s rival for the Germany No 1 shirt, Marc-Andre ter Stegen.
Neuer has been a regular for Bayern this season but has struggled to reach his previous heights since suffering a season-wrecking foot injury in 2017-18.