His father however said that the European Champions have not tried to make any contact with his son as of now and the only interest at the moment is from his ward.
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.
Chelsea insist no new contract offer has been made, because his current deal still has two-and-a-half years to run.
Real Madrid are seriously considering changing both of their main goalkeepers.
"Thibaut has a contract, also for the next season", said the Chelsea boss.More news: Christians mark Christmas with due religious fervour
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).
The Chelsea winger, who joined from Lille in 2012, has been in excellent form this season and is considered by many to be one of the finest players in the Premier League.
He said: 'My answer is always the same: this is a private conversation between the club and the player, and the agent of the player.
"Me and my staff are proud to have him as goalkeeper". I see now only one way to improve my team - to continue to work with this mentality, this desire, this will.
Emulating the exploits of Madrid's five-time Ballon d'Or victor Ronaldo and his Barcelona counterpart Messi is something a player of Hazard's considerable talents can plausibly aspire towards more than most, but Conte sees room for improvement for a forward with eight goals to his name across 25 appearances in all competitions this season.
CHELSEA face Stoke at Stamford Bridge on Saturday - here is our predicted line-up for the Blues. "It will be very important to continue with these types of players especially for your ambition to try to compete for something important". Conte admitted finishing in the top four would represent a successful season.