Chelsea are understood to have started looking at potential coaches to take over in case the Italian leaves in the summer.
When asked about his future on Friday, Conte said: “Everything is possible. I have another year of the contract, but as you know very well in football everything is possible.
"In one moment you stay here or another moment you stay at another place, or another person replaces you in your job.
“I know very well that football is this. Our job is very difficult, everything can change. From the start of the season people have been repeating the same question. At one point I have to tell you 'okay, if you want to sack me, it's okay'. But I'm always telling the same things.
“For this club it's normal. For a manager of this club it's normal to have this type of situation. This is the history of this club for the manager. I have a lot of experience to live with this type of situation.
“But something is strange that after the first game we lost against Burnley (they lost 3-2) the press pushed quickly to sack me for another coach. At other clubs this doesn't happen.
“You must trust in your work, trust in what we're doing, what we have done in the last season and a half. But in football anything can happen, we must be ready. But never give up."
Conte won the League and reached the FA Cup Final last term, but asked if the continued speculation shocks him, he replied: “No, I am not surprised.
“I don't ask to change the situation. My only problem is to continue to work, to do my job, be professional, have good results, then to continue my idea."