Conte lifted the FA Cup on Saturday as his side beat Manchester United 1-0 at Wembley, thanks to Eden Hazard’s penalty.
The Italian has fallen out with Chelsea’s hierarchy on several occasions over the club’s transfer policy, as well as the handling of players within the squad.
According to the British newspaper, other managers on Chelsea’s wanted list are Monaco chief, Leonardo Jardim and Napoli Supremo Maurizio Sarri.
Speaking about his Chelsea’s future after winning the FA Cup trophy, Conte told reporters: “Sometimes you do not always have the same ambition.
“Last season after we won the League, I and the club spoke, we tried to find the right way to try to defend our title. I decided to stay and work hard.
“When you decide to take on a coach like me, you must know who you are taking on, who you are charging for this job. I cannot change my personality, my idea of football. I am a serial winner.
“The way we played on Saturday was the only way to lift a trophy the way we are now. If you want to change, you must change many players.”
“I don’t think winning the FA Cup changes anything about my future. A win or a loss cannot change that.
“It’s right for the club to take the best decision. The win on Saturday cannot change an assessment of my work.
“We could have played better at Wembley but the situation is we have to play strong defensively if we want to win a trophy.
“The club has the right experience to understand the moment now and what the club has to do in the future, to be competitive and to fight for a place in the Champions League.”