Sky Sports and the BBC reported on Friday that Firmino has decided to leave the Reds on a free transfer rather than extending his contract.
Firmino, who has scored 102 goals in 352 appearances for the club, was fundamental to Liverpool's rise back to the top of the English and European game under Jurgen Klopp.
He has won several major honours in the Champions League, Premier League, Club World Cup and FA Cup since joining from Hoffenheim in 2015.
The Brazilian, however, has fallen down the pecking order in recent seasons due to the arrival of Diogo Jota, Luis Diaz, Darwin Nunez and Cody Gakpo at Anfield.
Firmino is one of five Liverpool players out of contract in the post-season ahead of a major rebuild.
Midfielders Naby Keita and Alex Oxlade-Chamberlain also expected to leave.
The futures of James Milner and third-choice goalkeeper Adrian remain unclear.
