Conte also said he felt he could help Hazard hit the goal-scoring heights if he stayed at Chelsea.
"If you are in a great club and you have trust in the club and the ambition of the club, I think it's right to stay", Conte said.
Courtois' two young children from a previous relationship still live in Spain where he spent time on loan with Atletico Madrid.
Chelsea have prepared a Plan A and Plan B for the 25-year-old, and Plan B sees the Premier League champions ready to hand Courtois a new contract that would make him the highest-paid goalkeeper in the world.
"My only hope is to continue to train him because I'm very happy for his commitment, his behaviours and the atmosphere they have created with the three goalkeepers and the two goalkeeper coaches". Juventus are demanding £25 million, rejecting Chelsea's £17 million bid for a player who has not been afforded many opportunities under Max Allegri this season, with 15 appearances in 34 matches.
And though Ederson's pass completion (87.4 per cent) towers above other Premier League goalkeepers, Courtois' rate (71.3) far outweighs former Real target De Gea's (55.3).
Asked about Hazard, he replied: "My answer is always the same: it's a private conversation between the club and the player and the agent of the player. He's a really good guy, he has a lot of space for improvement to become one of the best in the world". The pressure will be on him to deliver, having seen James being relegated to the bench for his inconsistency, and he will have improved his mental strength after last season, to move to a club the size of Madrid and deliver.
Conte also dismissed the suggestion that Courtois wants to move back to Spain simply because of his family connections.
"The family is not the problem. Because, I repeat, I can tell I have fantastic players with me".
Conte is also happy to leave recruitment matters in the hands of Chelsea officials, although he recognises the transfer window next month is a key time for the Premier League champions to strengthen.
"It doesn't change. For us, I repeat, it's very important to look at ourselves and then try to find the right way to improve", he said. For sure, the club will try to do their best to improve the squad and the numerical aspect. My task is on the pitch.
And while Conte has admitted he has no power over keeping Hazard, with the club's board of directors taking a leading role in negotiations, the Italian has made it clear that he wants to see his best players remain at the club.