According to a report from Corriere Dello Sport, Juventus are interested in signing the Brazilian international striker, and the move is reportedly very close.
The report adds that Juventus have already submitted an offer of around £19 million for the Liverpool striker, and the player is open to the idea of joining the Italian club to play regular first-team football.
Liverpool signed Uruguay international Darwin Nunez for a club-record fee earlier in the summer, and the 22-year-old is expected to be the first-choice striker at Anfield next season.
Firmino is likely to play as a squad option, and it seems that the Brazilian could look to move on in search of a starting role at another club.
The 30-year-old has been a remarkable servant for Liverpool, and he has helped the club win the Premier League and the Champions League, among other trophies.
There is no doubt that the Brazilian has regressed over the last couple of seasons in terms of his goalscoring ability, but he still remains a world-class footballer. He can play across multiple positions and provide valuable contributions to the team.
Moreover, the Brazilian has a leadership role in the group, and Liverpool will need his experience and mentality in their quest for silverware next season.
It would be quite surprising if the Reds decided to sell him this summer, especially this late in the window.
The Reds will begin the season on Saturday against Manchester City in the Community Shield, and it seems highly unlikely that Jurgen Klopp will sanction the sale of a key player without having signed a potential replacement already.
Furthermore, Liverpool have already sanctioned the departure of Sadio Mane this summer and letting another key attacker leave, is simply out of the question.