Firmino had missed training at Melwood on Monday due to a virus, but was able to join up with his team-mates ahead of this evening's game.
The news will come as a fillip for Klopp, who is already preparing to use midfielder Fabinho as an auxiliary centre-back for the last-16 first-leg tie at Anfield.
Dejan Lovren is unlikely to feature having sat out of yesterday's training session, the Croatian not yet recovered from a hamstring injury sustained last month.
Firmino, though, is expected to start in a three-man attack with Sadio Mane and Mohamed Salah, meaning the Brazilian will maintain his record of featuring in all 34 of Liverpool's European games under Klopp.
Centre-back Jerome Boateng won't be available, however, and was absent from the travelling party heading to Liverpool due to illness.
Klopp's men were beaten three times in the Champions League group stages, although a 1-0 win over Napoli in their final game ensured they qualified for the last 16 behind PSG.
Bayern, meanwhile, won four of their six group games, scoring 15 goals in the process, with Robert Lewandowski currently the tournament's top scorer for the 2018-19 campaign with eight to his name.
The Bavarians haven't had it all their own domestically, however, with Bayern currently trailing Dortmund in the Bundesliga title race, although they have managed to cut the gap to just three points over the past round of fixtures.
Liverpool last faced Bayern in the Audi Cup back in 2017, with goals from Mane, Salah and Daniel Sturridge securing a 3-0 win for the visitors.
The Reds also claimed a 3-2 UEFA Super Cup win over their German opponents in 2001, John Arne Riise, Emile Heskey and Michael Owen on target in that game at the Stade Louis II.