D'Antoni, 68, told Rockets owner Tillman Fertitta and general manager Daryl Morey he wants to keep coaching the Rockets for at least three more seasons, according to ESPN's Adrian Wojnarowski.
"I want to be a part of a championship here," D'Antoni told ESPN.
D'Antoni is 628-499 in 15 seasons. He is 173-73 in three seasons with the Rockets.
D'Antoni would become the oldest head coach in modern NBA history if he coaches another four seasons. Hubie Brown stepped down from coaching in 2005 only months shy of turning 72.
D'Antoni will turn 72 in May 2023.
Fertitta told the Houston Chronicle last week that he plans to talk with D'Antoni this summer.
"Mike and I do well together," Fertitta said. "Hopefully, we'll continue to win and Mike will be here for a long time."
Houston went 53-29 this season. The Rockets lost to the Golden State Warriors in the NBA Western Conference Semifinals.