Neuer’s contract expires next summer and the 40-year-old is expected to end his long career at Bayern Munich, while Sven Ulreich could also leave the club.
That would leave Bayern needing to strengthen their goalkeeping department, with Urbig regarded as the intended successor to Neuer as the club’s first choice.
According to Sky, Baumann is among the candidates being considered to provide experienced competition and cover for the 23-year-old.
The 36-year-old is highly regarded at Bayern, while supporters have also reportedly favoured him as the preferred option. However, Bild reports that there has been no concrete contact between Bayern and Hoffenheim so far.
Baumann’s age could also count against him as Bayern look to find a goalkeeper who can provide greater long-term security.
The Hoffenheim captain is under contract until 2027, with an option that could extend his deal by another year. He is also not currently considering leaving the club, where he remains the established first choice.
Bayern are therefore considering younger alternatives as they plan for the post-Neuer era.
Fulham goalkeeper Bernd Leno, Augsburg’s Finn Dahmen, Hamburg’s Daniel Heuer Fernandes and Cologne’s Marvin Schwäbe are among the other names under consideration.
Leno, 34, has previously been linked with Bayern and is also approaching the final year of his current contract, potentially making him another attractive option.
Bayern’s priority is understood to be finding an experienced goalkeeper who can support Urbig without disrupting plans for the youngster to take over as number one.
That makes the recruitment decision particularly important as Bayern prepare for one of the biggest changes to their squad in years.
Neuer has been Bayern’s first-choice goalkeeper for more than a decade, but the club are now actively assessing the market for the player who can help them through the transition.