Kuyt is a Holland teammate of Sneijder.
"I spoke to him over the last few days and I think he appreciated what I had to say," Kuyt told Milliyet.
"Fenerbahce are interested in Sneijder and monitoring the situation. We know he is a very expensive player and there are many important clubs who want him, but we will give it our best shot.
"This transfer would be fantastic for us. He is making a decision, but I don't know what he's thinking."