Conte arrived on a three-year deal last summer but is now looking beyond that.
The Blues have planning permission to rebuild their ground, though they are yet to decide whether to proceed.
"This could be a fantastic challenge for me and also for the club - to stay together and to play with this team in a new stadium," said Italian Conte.
The last manager to have four calendar years in charge of Chelsea was John Neal between 1981 and 1985.
"I want to break this bad record. I must be positive," added Conte, who steered the Blues to the Premier League title in his first season.
"When you start a job with a new club, I hope to stay in this club for many years. Honestly, the new stadium will be great - but I love Stamford Bridge a lot.
"Stamford Bridge is like my house."
Chelsea have been given permission by the mayor of London to build a new £500m 60,000-seat stadium.
If they do rebuild Stamford Bridge they will probably need to temporarily relocate, with Wembley the most likely destination.
The national stadium is Tottenham's home this season while White Hart Lane is redeveloped, and Spurs host Conte's side in their first Premier League home game there on Sunday (16:00 BST).
Conte took charge of former club Juventus in 2011 as they moved into a new stadium. They had left their former Stadio delle Alpi home in 2006 and shared the Stadio Olimpico with local rivals Torino a ground for five years.
"For sure, it's not the same when you play not in your stadium," Conte added.
"But if you want to have another good step to improve the club, you must have this type of situation."