According to Sky, the 31-year-old Stuttgart goalkeeper has been offered to Bayern, where he could be considered for a role as the experienced deputy to Jonas Urbig.
Bayern Munich are preparing for the possibility that Manuel Neuer and Sven Ulreich will retire at the end of the current season. Urbig, 23, is expected to take on a more prominent role, but the club are also looking for an external option to provide cover and competition.
Several established goalkeepers have already been linked with the Munich side, including Oliver Baumann of Hoffenheim, Augsburg's Finn Dahmen, Marvin Schwäbe of Cologne, Fulham's Bernd Leno and Hamburg's Daniel Heuer Fernandes.
Bredlow would fit the profile of a goalkeeper willing to accept a supporting role rather than immediately challenge Urbig for the starting position. However, Bayern have not yet shown a clear willingness to pursue the Stuttgart player.
Sky reports that the Munich club are currently considering other candidates, leaving Bredlow's prospects uncertain.
The goalkeeper has spent several seasons at Stuttgart and has been a dependable member of their squad. His situation has nevertheless become less settled, with competition for places shifting again following the return of Dennis Seimen.
Bredlow is now back in the role of second-choice goalkeeper at Stuttgart, prompting speculation about whether he could seek a new challenge elsewhere.
His contract has entered its final year, which could make the coming months important in determining his next step. A move to Bayern would offer the opportunity to join one of Germany's biggest clubs, although the prospect of limited playing time would be a significant consideration.
Bayern Munich's search reflects the wider transition facing their goalkeeping department. Neuer remains a major figure, but the club must plan for life beyond the veteran, while ensuring Urbig has experienced support as he develops.
For now, Bredlow is one name in a wider group of possible candidates. Bayern's interest has not advanced into a confirmed move, and the club's eventual choice will depend on how they want to balance experience, availability and the needs of their emerging first-choice goalkeeper.