The Houston Chronicle first reported details of the trade on its Web site on Tuesday night.
Artest's long-anticipated move out of Sacramento probably can't be announced yet because Greene, acquired by the Rockets on draft night last month, signed a contract with Houston on July 14. A player can't be traded within 30 days of signing a contract, according to league rules.
Rockets general manager Daryl Morey did not immediately return a phone message. Rockets spokesman Nelson Luis said Morey was traveling out of the country and unavailable for comment. Morey planned to attend the Olympics next month.
The Kings confirmed that the teams had spoken about Artest.
"We have had some very positive discussions with Houston involving Ron, but no trade is imminent at this time," said Geoff Petrie, the Kings' president of basketball operations.
The 6-foot-7, 248-pound Artest averaged 20.5 points last season, his highest since 2004-05, when he averaged 24.5 for Indiana. He also grabbed 5.8 rebounds per game for Sacramento last season.
The 28-year-old Artest is as well known for his volatile personality as his basketball skills. While playing for the Indiana Pacers, he was the central figure in the 2004-05 brawl with fans at The Palace of Auburn Hills during a road game against the Detroit Pistons.
He was suspended for 73 games, the NBA's harshest punishment for a fight. In December, two civil lawsuits against Artest that stemmed from the fight were dismissed.
Artest had surgery on his left thumb in April and was expected to take 8-to-10 weeks to recover. His summer has been just as turbulent as most of his NBA career.
After wavering for more than two months, Artest elected not to opt out of the final year of his contract for $7.4 million by July 1. But the forward immediately announced he regretted his decision, saying the Kings had misled him on their interest in a long-term contract extension. Artest also said he couldn't see himself playing in Sacramento beyond next season.
Artest apologized to the Kings a few days later after a long discussion with Petrie -- but one week after that, Artest demanded a trade, claiming he had been blinded to his career well-being by his friendship with the Maloof family, which owns the Kings.
Joe Maloof responded sharply to Artest, warning the forward to muzzle himself. Two weeks later, the Kings apparently found a taker for Artest's defensive skills and high-maintenance personality.
The trade will reunite Artest with Rick Adelman, who coached Sacramento when Artest was acquired by the Kings in a trade with Indiana during the 2005-06 season.
Artest played 40 games for Adelman and averaged 16.9 points, 5.2 rebounds and a career-high 4.2 assists. He was also named to the NBA All-Defensive first team.
The Rockets went 55-27 last season, but failed to get past the first round for the fourth time in five seasons.
The Kings, meanwhile, would be thrilled to get their hands on Greene, a 6-foot-11 forward from Syracuse who impressed the club in pre-draft workouts. Greene was drafted by Memphis with the 28th overall pick and traded to Houston in a three-team deal on draft night.
Although Greene played just one college season, he proved to be a versatile scorer who could fit well into Sacramento coach Reggie Theus' uptempo game plans.