Conte has only been in charge at Stamford Bridge since July, but he had to answer questions about his job security on Friday following heavy betting on his imminent dismissal 24 hours earlier.
Chelsea owner Roman Abramovich is notorious for acting quickly when he feels a manager is underachieving and last season he sacked Jose Mourinho eight months after his team won the Premier League.
But, although Chelsea have endured some difficult moments in the early stages of Conte's reign, including consecutive lacklustre defeats against Liverpool and Arsenal, it would be a bizarre move to axe the Italian after only nine games.
Chelsea have made it clear they have no intention of wielding the axe and Conte was relaxed when quizzed ahead of Saturday's Premier League clash with champions Leicester.
"I take this with a smile. I'm trying to find who bet the money!" Conte told reporters at Chelsea's training ground.
"I have good communication and a good relationship with the club.
"It's very difficult to talk about this situation. I'm focused about my work. I'm focused to improve the team. "
After spending the majority of his managerial career with Italian clubs, whose owners are famous for hiring and firing with remarkable regularity, Conte isn't fazed by his first taste of England's version of the sack race.
"The pressure is the same. It's normal to be under pressure, also for the players," he said.
"When you are in a club you want to win and do good work. The pressure is part of our job. It's the same in other countries.
"We are working very hard to change the situation of the past, the whole of the last season.
"We are trying to bring something important for the present and the future."
While he remains confident about his future with Chelsea, after failing his first two big tests against Liverpool and Arsenal, Conte can ill-afford to finish the next two matches without positive results.
Home games against Leicester and Manchester United will provide further evidence of how far Chelsea have come under Conte, who said: "These are two big challenges.
"Leicester won the title last season and are playing a good Champions League.
"Then with Manchester United they are another great team, but in this moment we must think about ourselves and not the other team."
Conte's major problem so far has been a shaky defence that had leaked goals at an alarming rate.
The former Juventus coach responded by switching to a formation with three central defenders and the result was a 2-0 win at Hull in their last game before the international break.
Conte will stick with that formation against Leicester, but he has to decide whether to keep faith with David Luiz, Gary Cahill and Cesar Azpilicueta or recall captain John Terry after he recovered from an ankle injury
"Yes, John is available, he came back for training in the middle of the week and did all the sessions," Conte said.
"It was necessary to find a solution because it is not right for a great team like Chelsea to concede so many goals in those games.
"Now I have four central defenders and one must go on the bench."
Conte also needs to get the best out of Eden Hazard, the mecurial Belgium midfielder who this week expressed a desire to be used by Chelsea in the number 10 role he enjoys with his country.
Showing no signs of bowing to Hazard's wishes, Conte said: "Now we are finding the best solution for the players and their talent.
"In the last game against Hull we played a good game. Hazard and Costa played very well and did what I want. Now we must continue this way."