The Bundesliga giants are looking to refresh their squad at the end of the season and Reds star Firmino is one of their top targets.
Boss Hans Flick believes the 28-year-old Brazilian is the ideal player to bring in to lead the attack with Robert Lewandowski who turn 32 this summer.
And with Manchester City's Leroy Sane still in Bayern's sights, the club are hoping a double raid on the Premier League will leave them with a front line to strike fear across Europe.
Jurgen Klopp is in pole position to win the race for signature of RB Leipzig sensation Timo Werner, 23, who is understood to favour a move to Anfield above any other options.
That leaves Firmino's role with the European champions under threat and Bayern are ready to test Liverpool's resolve with an offer this summer, which could be as high as £75million.