The former Reds forward returned to Anfield on Wednesday night to see his old club impress in beating Red Star Belgrade 4-0 to move top of Group C in the Champions League.
In the Premier League, meanwhile, Jürgen Klopp’s team are unbeaten in their opening nine games and only reigning champions Manchester City can match their tally of 23 points.
Kuyt, who scored 71 goals in 285 appearances during six seasons with the club, was part of the Liverpool side that fell narrowly short of winning the title in 2008-09.
He later concluded his career in fairytale fashion by scoring a hat-trick to seal the Eredivisie championship for Feyenoord in May 2017.