The Rockets also get first-round draft picks from both teams and ship rookie guard Ish Smith to the Grizzlies.
The person spoke to The Associated Press on condition of anonymity because the Rockets have not officially announced the trades.
Houston is 28-31, 11th in the Western Conference. General manager Daryl Morey has said in recent weeks that virtually every player on the roster was in play for trades leading to Thursday’s deadline.
Brooks and Battier have contracts expiring after this season, coveted commodities for teams looking to create salary-cap space. But in acquiring the 7-foot-3 Thabeet and Dragic, the Rockets are parting with two of the team’s most popular players among fans.
Brooks was a first-round draft pick by the Rockets in 2007 and shined in the 2008-09 playoffs. The 6-footer averaged 16.8 points and 3.4 assists and nearly led Houston to a second-round upset of the Los Angeles Lakers. He was honored as the NBA’s most improved player in 2009-10, but a sprained ankle limited his production earlier this season and he wound a reserve, backing up Kyle Lowry.
Unhappy with his playing time, Brooks left the bench during a game against Memphis on Feb. 5, and the team suspended him for a game. He was averaging 11.6 points and 3.8 assists, far below his 2009-10 averages. He was also shooting 28.4 percent from 3-point range, a career-low in his four NBA seasons.
The 24-year-old Dragic is averaging 7.4 points and 3.1 assists this season, but he’s shooting only 27.7 percent from 3-point range. Dragic has a team option for the 2011-12 season left on his contract.
Battier, 32, is valued as much for his play and leadership as for his contract. He’s to make about $7.4 million this season.
Memphis originally selected Battier with the sixth overall pick in the 2001 draft. He played five seasons in Memphis, helping the Grizzlies to three playoff appearances, before he was traded to the Rockets in July 2006 for Stromile Swift and the draft rights to Rudy Gay.
The 6-8 Gay, the Grizzlies’ second-leading scorer (19.8), is expected to miss about three more weeks after dislocating his left shoulder Feb. 15.
Battier has started all 59 games this season and averaged 8.6 points and 4.8 rebounds. He’s also the team’s top active shot blocker and its third-best 3-point shooter (39.5 percent).
The 7-foot-3 Thabeet has disappointed since Memphis took him with the second overall pick in the 2009 draft. He’s to make about $4.8 million this year and $5.1 million next season. The Grizzlies held the option for the 2012-13 season.
Thabeet, born in Tanzania, attended high school in Houston before playing for Connecticut from 2006-09. He’s averaged only 1.2 points and 1.7 rebounds in 45 games this season.
But the Rockets have been desperate to add size since Yao Ming went down early in the season with a stress fracture in his left ankle. Chuck Hayes, at 6-6, is the shortest starting center in the NBA and 7-foot Brad Miller, acquired in the offseason to back up Yao, missed 15 games with a knee injury.
Smith, a 6-foot rookie out of Wake Forest, has bounced between the Rockets and their developmental league affiliate this season. He averaged 2.6 points and 2.3 assists in 28 games with Houston this season.
