Leinart, 28, suffered a season-ending collarbone injury Nov. 27 while making his first start in place of Matt Schaub -- who had been lost for the season with a foot injury.
Leinart, the 2004 Heisman Trophy winner for USC who was drafted 10th overall by the Arizona Cardinals in 2006, re-signed with the Texans last offseason after not taking a snap in 2010. He turned down other offers to return to Houston because he was comfortable with coach Gary Kubiak and his offensive system.
Leinart was released by the Cardinals in 2010 after a rocky stay in which he never lived up to expectations that he would seize the starting quarterback job.
"I was surprised," he told the newspaper. "They told me they were up against it (salary cap), and they didn't want to insult me by asking me to take a pay cut. They said they hated to do it, and maybe we could work something out, but, well, I'm just stunned. I didn't want to leave. This just sucks."