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The 31-year-old was the club's top-scorer last season but has struggled to find the net consistently this term.
However, his work ethic has endeared him to the Anfield faithful and the management staff, who appreciate his contribution to the team.
Dalglish has juggled his pack on several times this season and the Dutch forward has found himself in and out of the side.
This had given Roma and Fiorentina hope they might be able to lure the former Feyenoord striker to Serie A, but the Reds have dismissed their interest.
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Kuyt's agent Rob Jansen told Dutch newspaper De Telegraaf: "There were quite a lot of clubs across Europe who are interested in Dirk, along with some Italian clubs.
"But Liverpool won't let him go."
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