The attacker found fewer opportunities in the Reds' starting line-up as the 2011-12 season progressed and has been tipped for a return to his former side Feyenoord this summer.
After being shifted out to the flanks in recent years, the 31-year-old has found competition from new singings such as Jordan Henderson, Stewart Downing and Craig Bellamy, and believes that, under Dalglish, he will be restricted to fewer games and will struggle to flourish under the Scot’s current rotation policy.
"Under this manager I don’t have the feeling any more that he will put me in the side every week," Kuyt told The Sun.
"I'm under no illusion about playing every week but I believe I am still good enough to play for Liverpool every week.
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"My physical stats are better than ever before. Last season I was scoring goals all over the place. But this season the manager bought three players who all played in my position.
"In the rotation system he used, I never found my rhythm again and never felt my old self.
"Deep in my heart I’d love to stay at Liverpool so I could have full revenge on everyone in my final season at the club."
Both Roma and Hamburg have shown interest in the Liverpool man, but Kuyt conceded that he could not take up an offer from Feyenoord, the side who sold him to the Merseyside club, due to the poor standard of the contract on the table.
"Clubs from real big leagues are knocking on the door," he added.
"I've turned down an offer from my old club Feyenoord for financial reasons. I’d have to take an 80 per cent wage cut."