Kuyt is set to feature for the Netherlands at the World Cup final against Spain on Sunday.
The Dutchman has previously hinted that he could leave Anfield.
“Of course I want to stay,” said Kuyt. “Liverpool is a great club with a great history.
“Unfortunately in my four years I haven’t won anything but hopefully in the future, I will still have that chance.
“We will have to see what happens but hopefully the manager wants me to stay.
“I spoke to people at the club and I know he wants to speak with me. But it is very difficult at the moment because we are so busy and focus on what lies ahead.”