As Standard Sport revealed yesterday, Conte has publicly stated that he has no interest in going to Inter Milan and is happy at Stamford Bridge.
Chelsea handed the former Italy coach a three-year contract when he took over last summer, but plan to hand him an extension at the end of the season.
Conte is the 10th different manager to be employed by Roman Abramovich since he bought the club in 2003 and the owner has a habit of losing patience with coaches when results go awry.
But Conte said: “The story tells us this, but I'm not worried about this. I want, with my players, to work very hard. I trust very much my work.
“We have to continue in this way, to work very hard and try to do something important this season. We are in the right position and we have the possibility to continue in this way.
“I think my situation is very clear. I have a contract with Chelsea. We are trying to build something important with the club, for the present and for the future. I think the situation is very clear.
“When you start working at a new club, you hope to stay many, many years because it means you are working very well.
“You have the possibility to improve your players, to improve your team, and to grow together. I think this season we are doing this.
“We are putting a great foundation down for the present and, above all, for the future.”
Conte looks on course to win the title in his first season in charge. The club are 10 points clear in the Premier League, but Conte suggests the best is still to come.
“In this moment, it's a (season of) transition at Chelsea,” he said. "A season where a lot of players who won a lot here have changed teams.
“But you know, especially with things fresh from (the sacking of) Claudio Ranieri. You have to be ready for anything. But if you ask my opinion, I hope to stay and work a lot for this club, to win a lot with this club.”
The 46-year-old admits the toughest thing he’s dealt with so far is the fact his wife and daughter are still living in Italy.
Plans are afoot to move them to London during the close season and Conte said: "The only problem for me this season was the family missing me. For sure, my family stayed in Italy. I'm working, and working for the future to try and bring them here and to stay together. Family is missing me, this is the truth.”