There had already been suggestions he would walk away and now multiple sources including Sky Sport Deutschland and Sky Sport Italia all confirm the decision has been made.
He was offered a new contract to remain at Anfield, but believes it is the right time for a new challenge.
That could well be in Serie A, where Firmino has fans in the form of Juventus, Inter and Milan.
The Rossoneri in particular are known to be looking for a reliable centre-forward at low cost, in the same mould as Olivier Giroud, as Firmino’s former Liverpool teammate Divock Origi has barely featured due to injury problems.
The Brazil international is 31 years old and has been at Liverpool since 2015, previously featuring for TSG Hoffenheim, Tombense and Figueirense.
So far this season, ‘Bobby’ has scored nine goals and provided four assists in 25 competitive matches for Liverpool. He has 55 senior caps for Brazil, in which he contributed 17 goals for his country.