Kuyt's current contract expires at the end of next season but he is already in talks over a new one.
"My contract has one more season to go after this but there are things happening," said the Dutch international.
"We have had some talks and I can only say it looks positive.
"I feel at home in Liverpool and I don't want to leave here.
"It has been a difficult time for everyone at the club with the changes that have happened since last summer but now I can sense something good is happening - I think Liverpool are on the way back."