The Brazil international has spent the last eight seasons at Anfield after joining from TSG Hoffenheim for £29m in the summer of 2015.
At a point, the 31-year-old formed part of a fearsome attacking trident that included Sadio Mane and Mohamed Salah.
They terrorised opposition defenders in England and abroad, bringing to Anfield the UEFA Champions League trophy, Premier League, FA Cup, League Cup, UEFA Super Cup and FIFA Club World Cup.
While Salah signed a new contract last summer, Mane departed for Bayern Munich and Firmino is next in line to exit.
Firmino has made 353 appearances for Liverpool in his time at the club, scoring 107 goals and providing 78 assists.
He has become the highest scoring Brazilian in the history of the Premier League with 78 goals.
Firmino has scored nine goals and provided four assists in 26 appearances for Liverpool this season but missed out on Brazil's World Cup squad and has struggled with injury recently.
Firmino was in negotiations with the Reds over a new contract but has now decided to explore a new challenge elsewhere and will leave as a free agent.