The Belgium captain has two-and-a-half years left to run on his current deal but his father Thierry Hazard had claimed that he has rejected a contract from Chelsea, as he aims to keep his options open for the summer with Zinedine Zidane's side interested in his services.
The former Lille winger has not in fact been offered a deal yet by Chelsea, though the Stamford Bridge club are known to be prioritising their efforts to keep Hazard.
Conte admits that he is keen to see the 26-year-old stay after being asked about Hazard Snr's interview with the French publication Le Soir.
“My answer is always the same: this is a private conversation between the club, the player and the agent of the player," he told reporters on Friday. "The same speech for Eden. 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.”
Chelsea are faced with a pressing issue of renewing Thibaut Courtois' contract as well, with the keeper having a year less to run on his deal than Hazard, and the club are similarly looking to get him to sign in the coming months.
Conte doesn't believe that his shot-stopper is pushing for a move for family reasons despite Courtois previously admitting that he might be interested in a move to Spain - in particular Madrid - where his family currently live.
“Courtois has a contract, also for next season, 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, and proud to create this synergy, this link between three fantastic goalkeepers with Thibaut, Willy Caballero and Eduardo.
"I'm very happy to have these three players. There is great synergy with these three players. For sure, I hope to have all the players for the next season."
“I don't know [if he wants to move back to 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. I think the family is not a problem.
"My only hope is that I continue to train him because I'm very happy with his commitment, his behaviour and the atmosphere the three goalkeepers have created."