But current Rockets center Omer Asik wasn't one of them.
Shortly after Howard announced his decision to play in Houston, Asik contacted the Rockets asking to be traded, according to an ESPN report, but the team has turned down his request and has no plans to move him.
Asik is reportedly unhappy about his playing time and role being diminished. Howard and Asik are both traditional low-post centers.
Following Howard's decision, it was also widely reported that Asik and perhaps even Jeremy Lin might be on their way out of town in a sign-and-trade deal with the Atlanta Hawks to bring Josh Smith to Houston. However, that ship sailed after Smith agreed to a four-year, $56 million contract with the Detroit Pistons.
Now the Rockets and head coach Kevin McHale seem committed to keeping the disgruntled Asik, hoping to mend any fences that may have been damaged.
"With Omer, he had a great year for us last year and really became one of the top centers in the league," McHale told ESPN.com. "It's just when you have an opportunity to get Dwight, it's hard not to. I'm sure Omer right now is a little down in the dumps, but we'll pick him up."
The Rockets signed Asik before the 2012-13 season as a restricted free agent after the 7-foot Turkish center played his first three seasons in the NBA with the Chicago Bulls. He averaged 10.1 points, 11.7 rebounds and 1.1 blocks for Houston while starting all 82 games.