However, the 31-year-old has said that he is not thinking of moving on any time soon.
"I can see myself staying at Anfield for the rest of my career," The Mirror quotes Kuyt as saying. "As long as I play as much as I want to play then I will be happy.
"If it gets to the point where I am not playing every game anymore, then maybe I will have to make another decision – but I don't think about that at this stage."
Kuyt joined the Reds from Dutch side Feyenoord in 2006.