The Brazil international completed a £39m move to the Reds from Ligue 1 side AS Monaco on Monday evening to become the German head coach’s first summer signing.
Fabinho will be tasked with improving Klopp’s midfield options in the middle of the park given continued uncertainty surrounding Emre Can’s future at Anfield.
Liverpool FC already have one Brazilian in their ranks and Firmino has excelled under Klopp in the current campaign.
Firmino has scored 26 goals and has made 14 assists in 52 games in all competitions in the 2017-18 season to produce his best return in a Liverpool FC shirt.
The 26-year-old has been talked up as one of the best all-round forwards in world football following his progression under Klopp.
Speaking to Liverpool FC’s website about his decision to move to Anfield to work with Klopp, Fabinho was asked whether Firmino’s improvement was a motivating factor.
Fabinho said: “I’ve been following Liverpool for a few years, in particular since Firmino arrived.
“After he arrived here, he was able to achieve higher development at this football club. Because he had success, I hope the same happens to me.”
Liverpool FC finished in fourth place in the Premier League table to secure their continued participation in the Champions League for a second successive season.
The Reds lost 3-1 to Real Madrid in the Champions League final in Kiev last weekend.
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