The Bavarian giants are expected to submit an offer to the Florence-based club at some point soon.
The Italian midfielder's price tag is in the region of €18.5 million.
Montolivo's arrival at the Allianz Arena depends on whether Russian club Anzhi Makhachkala purchase Anatoliy Tymoshchuk from Bayern for €11 million.
With clubs like AC Milan also reported to be interested, Fiorentina will be hoping to create a bidding war, rather than being forced to lower their price as Montolivo enters the final 12 months of his contract.
The 26-year-old's style of play and role is somewhat similar to that of Bayern midfielder Bastian Schweinsteiger's. However, the player has a fairly weak physical frame and may not adapt easily to the Bundesliga.
Although the Italian seems set to leave Fiorentina, many find him better suited to another club in Serie A.