The 26-year-old's current contract expires in June 2020 after the Brazilian arrived at Anfield for £21.3m from Bundesliga club Hoffenheim in 2015.
He has since become a prominent player in Jurgen Klopp's squad scoring 30 goals in 76 appearances.
However, his future at the Merseyside club has been made murkier following the departure of close friend Coutinho, whose transfer to Spain was confirmed a few days ago. In a farewell Instagram post, Firmino said that Liverpool "is no longer the same".
Liverpool will want to hang on to their striker, who has spearheaded the attack this season with 16 goals in 30 appearances, especially with the race for the Champions League places heating up. The 'Reds' currently sit in fourth place but face unbeaten league leaders Manchester City on Sunday which could prove to be a pivotal fixture.