Despite Chelsea claiming six wins from their last seven games, Fabregas knows they need City to start dropping points to give them any chance of retaining their crown.
Speaking to his media conference ahead of Chelsea's home clash against Atletico Madrid in the Champions League on Tuesday night, Conte talked up the importance of Fabregas to the west London side.
The 30-year-old finished the 2017-18 Premier League season with 13 starts and 16 substitute appearances in Chelsea's title-winning campaign under new boss Conte.
"You can just give up and accept you're not part of the team or the club in the future or what I did, put your head down, be humble, work hard, train hard every day, show him that he's wrong and that he can can trust me and play in this team". 'Physically, I feel, not better than ever because it's been many years and don't remember exactly, but the fittest I've been in the last few years. We will try our best to reach the final and hopefully win'.
I am only 30. I'm very young. I really mean it. I'm enjoying my football.
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Atletico, twice runners-up in the last four years, must win at Stamford Bridge and hope Roma drop points against Qarabag to avoid an early exit.
The Spaniard was initially not fancied at all by Conte, who did not believe he was a good fit for the defensive responsibilities involved in his favoured 3-4-3 system.
"When you are 30 years old you have at least five more years", said Conte. He's a victor in his mind, in his mentality.
Fabregas has won nearly every major honour in his storied career with Arsenal, Barcelona, Chelsea and Spain, including the World Cup - but the European Cup is the exception.
Costa will be eligible to play for Atletico from January, when their transfer embargo is lifted.