Kuyt played for the English club from 2006 to 2012, scoring 71 goals and providing 40 assists in 285 games.
After retiring, he took on coaching roles at Feyenoord U19, ADO Den Haag, and Beerschot VA.
However, it is expected that Kuyt will leave his current position this summer.
Liverpool is currently looking for a new assistant coach following the departure of Arne Slot's assistant, John Heitinga, who has joined Ajax as head coach.
