The Netherlands international cut a frustrated figure under Kenny Dalglish after being given limited opportunities and making several appearances from the bench, only scoring two Premier League goals this term.
And despite being linked to former club Feyenoord, with Roma and Hamburg also expressing an interest in the forward, Kuyt hopes to remain a Liverpool player next season.
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"I hope I can stay with Liverpool," he told Dutch newspaper Algemeen Dagblad. "But that's what I said the last couple of months."
The 31-year-old spoke out earlier this week of his frustration at being a fringe player under Kenny Dalglish, but now knows that things could change drastically with the appointment of a new manager at Anfield.
"With Dalgish as manager I didn't have the illusion he would let me start from the beginning [of matches] next season," Kuyt added.
"We have to wait and see now. I'm not sure yet what Liverpool will do with this manager vacancy."