D'Antoni, a two-time NBA Coach of the Year, has one year remaining on his current deal and prefers to have a new contract in place before the beginning of next season.
"I've let (general manager) Daryl (Morey) and (owner) Tilman (Fertitta) know that I'm energized to keep coaching - and believe that I can continue to do this at a high level for at least another three years," the 68-year-old told Wojnarowski.
"I want to be part of a championship here."
D'Antoni originally agreed to a four-year deal with the Rockets in June 2016. His salary, around $4 million per year, is far less than some of the league's top coaches, including San Antonio Spurs bench boss Gregg Popovich, who reportedly makes $11 million a year.
Houston is 246-173 in D'Antoni's three seasons at the helm. The team fell one game short of the NBA Finals during the 2017-18 season, losing Game 7 of the Western Conference finals against the Golden State Warriors.