Antonio Conte refused to discuss Eden Hazard's future despite claims from his father that he has rejected a new contract at Chelsea.
Hazard's father Thierry has told Belgian newspaper Le Soir that the offer of a new deal was turned down because of "interest" from Real Madrid.
Chelsea insist no new contract offer has been made, because his current deal still has two-and-a-half years to run.
Asked about Hazard senior's comments, Conte said: "This is a private conversation - between the club and the player, and the agent of the player.
"I'm proud to have him in my team, in my squad, and I'm very happy to work with him. He's a really good guy and has a lot of space for improvement, to become one of the best players in the world. But, I repeat, on this issue: this must be a private conversation between the player, the player's agent and the club."
The future of fellow Belgium international Thibaut Courtois also remains the subject of speculation, and Conte added: "Courtois has a contract, also for next season, with the club. With Chelsea. We are talking about one of the best goalkeepers in the world.
"Me and my staff are proud to have him as goalkeeper. For sure, I hope to have all the players for the next season.
"This is the type of conversation for the agent to have with the club. If you ask me if I hope Courtois stays? Yes, for sure. We are talking about a fantastic goalkeeper, a really good guy, and I'm happy to work with him."
"I don't know about this issue [surrounding Courtois' family living in Spain]. For sure, when you are in a great club and you trust in the project, you want to stay. You want to continue to play for this team. The family is not a problem. But I repeat, this is a private conversation between the player, his agent and the club. My only hope is that I continue to train him because I'm very happy with his commitment, his behaviour.
"You are talking about two important players for us. Yes, for sure, it will be very important to continue with this type of player, especially if your ambition is to try and compete for something important. It's very important to try to improve your team, to strengthen your team, and not to sell the best players."