The Brazil international scored twice in a 5-0 win against Swansea City at Anfield on Boxing Day to cement fourth spot.
He failed to find the net in Liverpool FC’s 2-1 win against Leicester City in their final game of 2017.
Firmino has scored nine times and has made four assists in 20 appearances in the Premier League.
The 26-year-old has netted 15 goals in 27 games in all competitions to produce his best goal return at Anfield to date.
However, Firmino has a tendency to miss one or two clearcut chances per game despite his impressive record.
Former Liverpool FC captain Redknapp has challenged Firmino to further improve his finishing.
“Firmino is such a talent but at times he can be even more clinical and score more goals,” Redknapp told Sky Sports.
Liverpool FC signed Bundesliga outfit Hoffenheim in a £29m deal in the 2015 summer transfer window under Brendan Rodgers.
Firmino has become a firm favourite under Jurgen Klopp and has managed to keep Daniel Sturridge out of the team.
The Reds signed four players in the summer transfer window to improve their squad ahead of a return to the Champions League.
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