Conte has enjoyed a stellar first season with the Blues, who sit 10 points clear at the top of the Premier League after 26 matches.
Reports this week linked the former Italy coach with a move to Inter, following previous claims he had failed to settle in the English capital.
But Conte, who signed a three-year contract with the club, remains committed to Chelsea and hopes the arrival of his wife and daughter will make him feel more at home.
"I am very happy for this experience because for me and my family it is incredible," he told Standard Sport.
"For sure, in this season my wife and my daughter stayed in Italy but I hope they come and stay here also because I need them.
"Yes, I hope [I can manage here for years]. Usually, when you start a project with a new team you want to stay many years and to build something important with the club.
"For sure, to build you must work many years to have the opportunity to grow with your players and to try to win also because when you are the manager in a great club, the imperative is to try to win but also to play great football.
"It wasn't easy for me when you arrive at the start of the season after a bad year. But I am pleased for the players because they showed me great commitment to fight and to come back very soon to fight for the title.
"The most important thing is the success of the club, the players and the manager. I was sure to arrive here and also to compete in this league with other good managers.
"Now, it is important to continue in this way because anything can happen until the end but we want to continue to stay on top of the table."
Chelsea visit West Ham hoping to extend their lead at the top of the table on Monday.