It was confirmed last month that Firmino will leave the Reds after eight years at Anfield.
And the 31-year-old has now agreed to join Barcelona on a free transfer, according to the Daily Mail.
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He had previously been linked with the likes of Roma and Real Madrid.
But reports suggest Firmino will join cash-strapped Barca when his Anfield contract expires at the end of the campaign.
Firmino joined Liverpool in a £29million deal from German side Hoffenheim in 2015.
In his time at the club Firmino has helped the Reds to Premier League, Champions League, FA Cup, League Cup and Club World Cup glory.
The forward made up one third of a formidable forward line alongside Mohamed Salah and Sadio Mane.
However, Firmino has seen his game time reduced this season as Jurgen Klopp overhauls his ageing squad.
The arrivals of Darwin Nunez and Cody Gakpo mean he has started just 12 games in the Premier Set featured imageLeague this term.
A hamstring injury means Firmino is reportedly set to miss the next three games, but Liverpool are hopeful that he can return before the campaign comes to an end.
Boss Klopp was claimed to have been keen for Firmino to extend his stay at Anfield, but the forward is eager to pursue a new challenge.
In total Firmino has played 360 games for Liverpool, scoring 109 goals and providing 79 assists.
