"He's very demanding in that he wants to win", Fabregas told Chelsea's official website.
Tuttosport reports that Conte has been offered a huge four-year contract worth €15 million ($21m) per season by Inter's wealthy Chinese owners the Suning Group.
'You have the possibility to improve your players, to improve your team, and to grow together.
"I've always wanted to play for this big club, it's one of the best clubs in the world at the moment and I'm enjoying every single minute".
The 47-year-old has brought fresh confidence among the Chelsea players this season, and this has transformed them into genuine challengers from what was a dismal 2015-16 campaign where they finished 10th in the league.
EDEN HAZARD trained with Chelsea today ahead of Monday's clash with West Ham.
So dependent are Chelsea on his heroics that Conte is fully aware of the need for additional cover in the position.
Aguero double helps City hammer Huddersfield after early scare
He added: "It is a breakthrough for the club to say that but I do not want to think about what will happen to my future. Meanwhile, Huddersfield boss David Wagner felt his side didn't demonstrate their best qualities at the Etihad Stadium.
Chelsea lost twice in September before a 13-game winning run in the Premier League ended at Tottenham on January 4.
"I can't wait to go to the London Stadium and, hopefully, we'll get three points".
"In my mind, there is the will to find different experiences in different countries", he said. Conte said that playmaker Eden Hazard has a minor injury but the Belgian should be fit for the game.
This week has also seen speculation over the future of Michy Batshuayi, the Belgium striker signed from Marseille for £33million.
Conte was asked about the situation on Friday.
"If he shows me he deserves to play I will put him in the starting eleven, if he doesn't then we will continue in this way".