The former Liverpool attacker has told his international colleague that Aykut Kocaman's side feels sorry for him at Inter and could offer him a way out of the Italian club.
Sneijder has refused to sign a new deal at the San Siro and looks unlikely to figure for the first team until he puts pen to paper, with a number of clubs, including The Yellow Canaries, eager to pull the 28-year-old away from the 2010 Champions League winner.
Former Liverpool winger Kuyt has revealed that he has tried to sell the idea of moving to the Sukru Saracoglu Stadium to his international teammate and he believes that the former Real Madrid playmaker could be interested in the transfer.
"It is to be expected that I speak to him often and I think he has been affected by what I told him and he liked it," he told Milliyet. "I told him that Fenerbahce sympathizes with his situation."
Kuyt also said that the capture of Sneijder would be an exciting move for Turkish football, although beating the likes of Manchester United and Bayern Munich to his signature could prove difficult.
"We know that Sneijder is an expensive player and there are other clubs that want him too," the winger went on. "I did not ask whether he will come here but I know there are people that wonder about him in Turkey.
"The transfer would be wonderful from our point of view. He has to make a decision but I don't know what he is thinking."