The club have already made two signings this summer, bringing in Ismael Saibari and Nathaniel Brown for a combined €110million to reinforce midfield and defence.
Bayern are now working on a further addition, with the club keen to add a new centre-back to their ranks.
According to La Gazzetta dello Sport, Bayern are in talks with Juventus over a move for Brazilian defender Gleison Bremer.
The 29-year-old has a release clause of €58million that is valid until mid-August, though Juventus could be willing to let him leave for less.
Reports suggest a fee of around €40million could satisfy the Italian club.
Bayern Munich have already offered €30million for Bremer, according to the report, and are likely to need to increase that bid to complete the signing.
Bremer would add further experience to Bayern's defensive options as head coach Vincent Kompany looks to strengthen his back line following last season's near miss in Europe.
The move would follow the pattern of Bayern's other summer business, with the club showing a clear intent to build a squad capable of going one step further in the Champions League next season.
Talks between the two clubs remain ongoing as Bayern look to finalise the deal before Bremer's release clause window closes in August.