"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.
Bill Paxton 'Training Day' Dedication Planned For New Episode
In a space of six months, Paxton went on to star in Twister , Apollo 13 , and Titanic . "He never lost track of who he was". The type that showed for every single occasion, no matter how small - Bill would be there.
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".