The 20-year-old has long been linked with Manchester United and Napoli.
Costa’s agent Cesar Bottega told notiziariosportivo.com: “I have spoken a few times with Manchester City.
“They have shown interest in the player and are now considering whether to enter into a negotiation or not.
“I am planning a trip to Europe in a fortnight, but if something were to change I’m ready to leave earlier.”
He added: “Napoli have followed the player’s performance in the Champions League, then I don’t know if there were concrete contacts, I have not been contacted.
“Logically, they will first, in any case, contact the company.”