Hazard's father revealed this week in an interview with Belgian newspaper Le Soir that his son is keeping his options open in the hope of encouraging interest from Real Madrid, who are long-term admirers of the 26-year-old and are coached by his idol Zinedine Zidane, at the end of the season.

Courtois, meanwhile, last month indicated that he wants to delay talks over a new deal until closer to the end of the season -- when he will enter the final year of his current contract -- while saying he is attracted by the prospect of moving to Spain to be with his two children.

Chelsea's position is that no formal contract offer has yet been made to Hazard, whose current deal runs until June 2020. Courtois' situation is more urgent, but Conte would not be drawn into commenting on any "private conversation" about either player in his news conference on Friday.

"My answer is always the same: this is a private conversation between the club and the player, and the agent of the player," Conte said when asked about Hazard. "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.

"Courtois has a contract, also for next season, with the club. 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. For sure, I hope to have all the players for the next season.

"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."

Asked if Chelsea could realistically stand in Courtois' way if he wants to join his children in Madrid, Conte replied: "I don't know about this issue. 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.

"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 and the atmosphere the three goalkeepers have created with the goalkeeping coaches. [I hope] to continue to see this situation for many years."

Conte has also voiced a desire to see Chelsea bolster their squad depth in the January transfer window, but he admitted that his involvement in any recruitment process next month will be limited as he focuses on matters on the pitch.

"I think the transfer market -- this window -- could be important if we are able to find the right players," he added. "Otherwise, we continue to work with these players. I'm very happy to work with them and, for sure, the club will try to do the best during the transfer market to improve the squad in the numerical aspect.

"But, at the same time, I'm a coach and I have to work with my players. My task is on the pitch. For the transfer market, there is the club. The club decide whether they want to improve the squad or the team. For me, I'm very happy to work with my players."

Conte's options have been boosted in recent days by the return of David Luiz and Charly Musonda to training at Cobham. He revealed both are "very close" to making full recoveries and indicated that next month's FA Cup third-round tie against Norwich City could be the ideal opportunity to put them back into first-team action.

Baba Rahman's return date, however, is less clear. The Ghana international has been sidelined since rupturing his ACL at the African Nations Cup in January and was not registered in Chelsea's squad list for the first half of the Premier League season as he continued his rehabilitation.

"This player is coming from a bad injury," Conte said of Rahman. "A bad, bad injury. He's struggling a bit to recover the best form. I must be honest, I don't know what will happen with Baba [in January]. For sure, about the human aspect, I'd like to give him an opportunity to come back strong like before. But I think that, now, he has to face his recovery.

"He is showing great patience because he's struggled a lot but, honestly, I don't know what will happen with Baba. If I can help him, I'm ready to help him. There is the player and there is the human aspect, to have a good rehabilitation. For him, it's good to stay here and recover, to take the right time to recover. And then we are ready."