The Italian is desperate to reach the Champions League, and his side’s chances of making it to the top four hang in the balance ahead of tonight’s north London derby.
Tottenham are four points behind bitter rivals Arsenal in fourth, and must win tonight’s crunch match and hope the Gunners slip up against Newcastle or Everton.
Spurs fans are fearful that if their side doesn’t reach the Champions League Conte could walk away, and Fabregas said his former manager is very capable of doing this.
Fabregas, who spent two seasons playing under the Italian at Chelsea, told LondonWorld: “I said as soon as he joined Tottenham, ‘unfortunately, Spurs have a really good manager on their hands.’
“He had a very difficult job on his hands when he took over at Tottenham with the team in a low position.
“I know Antonio very well, I have so much respect for him, we won a lot together and I can tell you that he is a serial winner. He will demand the best.
“Knowing him, if he doesn’t reach the Champions League or whatever objective he set at the beginning when he took the job, he’s capable of walking away.
“Not only because they failed, but because he will feel responsible. He will take it personally.”
However Fabregas was full of praise for his former boss, and said he could get by in management with everything he learned of Conte at Chelsea.
“I know exactly how Antonio works, I know this methodology very well,” he said.
“If I was a coach, I could get by managing with all that he showed me in the two years I worked with him.”
“Spurs are very well structured, they use the wing backs very high,” he said.
“They are intense and, a little bit like Arsenal, they try to build up from the back to draw the opponent out.
“Tottenham have world class players up front as well in Son, Kane and Kulusevski.
“Last weekend against Liverpool they gave them a game. If you’re going to beat a Conte team you’ll need to be very well structured.”
Fabregas advised Mikel Arteta to attack Spurs down the wings, as he said Conte likes to focus on crowding the middle of the park.
“We’ve seen many teams match his [Conte’s] system and go one-on-one across the whole pitch to see who is better,” he said.
“Teams used to do that against us at Chelsea. I don’t think Arteta will do that.
“I think he will go his way, he’ll play the 4-2-3-1, try to apply pressure from the front and try to have the ball. You need to switch sides constantly against Conte.
“If you try to play a lot in the middle, where he puts a lot of bodies and are very vertical, it will be tough.
“But if you keep switching sides, there will be moments where they’re not covered positionally and from there you can find spaces. It’s a good challenge for Mikel, for sure.”