The trio were reportedly targeted in an anonymous letter that was sent to the office of Bundesliga 2 side St Pauli on January 12.
The Criminal Police Office in Hamburg was informed and the threats have been taken very seriously, German publication Bild reports.
One of the alarming quotes from the letter read: "Save the league, save football. Fire and death to the dirty Bayern pigs."
Traces for DNA have been examined as well as fingerprints as officials look for the culprits.
It's understood threats were also aimed at Bundesliga referees.
Police spokesman Florian Abbenseth told BILD: "We're investigating on suspicion of threatening and disturbing the public peace through the threat of criminal offences.
"We're checking the backgrounds."
The DFB (German Football Association) and Bayern Munich have yet to make any comment thus far.
Bild's report added it's unclear why the letter was sent to St Pauli and if there are multiple individuals involved.
Bayern are six points clear at the top of the Bundesliga and are preparing for the first leg of their Champions League last-16 tie against Austrian side Red Bull Salzburg on Wednesday night.