The German club are said to have accepted an offer of £25 million which could rise with add-ons to £29 million.
Firmino has established himself over the past two seasons as one of the Bundesliga's most exciting players, with Manchester United also strongly linked for his services.
The reports piqued the interest of former Reds defender Jamie Carragher, who took to Twitter to discuss the signing.
Come on hipsters what's Firmino like?!!— Jamie Carragher (@Carra23) June 23, 2015
Rory it's the mystique let us dream!! https://t.co/c9mWteMmqV— Jamie Carragher (@Carra23) June 23, 2015
Signing a much-heralded Brazilian international with an eye for goal and creative spark? What isn't to love?
Liverpool's summer transfer business to date has been criticised so far even by their own fans as uninspiring, even if it may turn out to be effective.
Names like Danny Ings, Adam Bogdan, James Milner and Joe Gomez are not going to get the casual or devoted fans excited - but Roberto Firmino - now Liverpool have everybody's attention.