Cavani recently admitted the chance to work with City manager-to-be Manuel Pellegrini would be "a pleasure" following the news a player-plus-cash deal involving Edin Dzeko had stalled.
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"Cavani's intention is to play for Madrid," Luis Cavani told Futboleros.
"He is excited about it and is very willing to see it through. He has told the family in private that he wants to join Real Madrid but if he declares it publicly it will annoy Napoli.
"There has been contact with Real Madrid's lawyers and now we are waiting for the two clubs to meet. I hope it happens and that talks take place as soon as possible. Who wouldn't want to play for Real Madrid?
"It's not just up to Edi. They are talking about €65m (£55m) and Napoli won't negotiate for any less."
Cavani has scored 102 goals in 124 games since joining Napoli from Palermo in the summer of 2010.