The Houston Chroniclereported Sunday that the Texans might end up signing the former USC quarteraback, who was cut by the Arizona Cardinals on Saturday.
The Seattle Seahawks -- coached by Leinart's former coach at USC, Pete Carroll -- would seem like a natural fit for the quarterback, but they reportedly aren't interested, according to The Chronicle.
Matt Schaub and Dan Orlovsky are currently the only two quarterbacks on the Texans' 53-man roster. The team cut John David Booty on Saturday and haven't re-signed or added him to its practice squad as of Sunday.
Leinart entered training camp as the heir apparent to Kurt Warner in Arizona, but the former first-round draft pick lost his spot on the depth chart to newcomer Derek Anderson. The decision by the Arizona coaching staff led to a rift between player and team.
The Cardinals tried to trade Leinart, but they didn't find an acceptable deal. By cutting Leinart, the team doesn't have to pay him the $2.5 million that he was due for the coming season, not to mention the $7.4 million, plus a $5.5 million roster bonus, he was scheduled to make next season.
In other Texans news, a league source told NFL Network insider Jason La Canfora on Sunday that defensive end Aaron Schobel will not be coming out of retirement to join the team.
It had been reported that Schobel, a native of Columbus, Texas, was considering the move, but it is now believed that the 33-year-old isn't wavering on his decision to leave the game. He spent his entire nine-year career with the Buffalo Bills, receiving two Pro Bowl nods.
The Associated Press contributed to this report.