Kuyt scored just two goals in 26 Premier League appearances this season, with Reds boss Dalglish leaving the 31-year-old on the bench for large periods. However, Kuyt feels he is good enough to play on a more regular basis.
"Under this manager I don't have the feeling any more that he will put me in the side every week," Kuyt was quoted as telling 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.
"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."
His agent, Rob Jansen, added in Votelbal International: "We have already spoken to several interested parties, but no decisions have been taken yet. If Dalglish leaves, Dirk would be going nowhere."
Last month, Kuyt was seen having talks with Feyenoord technical director Martin van Geel, sparking reports he would sign for his former club. However, although the player admits he considered a move back to Rotterdam, he believes he still has much to offer a top European side.
"Deep in my heart I'd love to stay at Liverpool. The fact I held talks with Feyenoord indicates I wanted to give it a serious chance," he told AD Sportwereld.
"But in many ways the gap is too great at this moment in time. If I returned to Holland, I would have to take an 80% cut in my Liverpool wages."
Serie A side Roma and Hamburg in the German Bundesliga are believed to be interested in signing Kuyt once the summer transfer window opens.