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Houston quarterback Matt Schaub might end up with the Browns.

(AP)

CLEVELAND, Ohio -- It's a "serious possibility'' that the Browns will sign Texans veteran quarterback Matt Schaub to compete with Brian Hoyer, a league source told cleveland.com.

Schaub, an 11th-year pro, flourished under Browns offensive coordinator Kyle Shanahan in Houston, playing some of his best ball under the Browns' new playcaller.

A two-time Pro Bowler, Schaub spent three seasons with Shanahan in Houston in from 2007-2009, with Shanahan serving as his quarterbacks coach in 2007 and offensive coordinator in 2008-09.

The Texans might release Schaub, 32, because he's due to make $10 million in 2014. CBS Sports' Jason LaCanfora and nfl.com's Ian Rapoport have both reported the Browns' possible interest in the veteran passer. The Raiders and Jets are also reportedly interested.

In 2009, Schaub led the NFL in passing yards (4,770) and completions (396) that year, earning a 98.6 rating. He also earned Pro Bowl MVP honors.

Schaub, who knows the intricacies of Shanahan's West Coast system, would step in and compete with Hoyer, who's ahead of schedule in his recovery from a torn anterior cruciate ligament.

Schaub fell out of favor in Houston last season when he went 2-6 and threw 10 touchdowns and 14 interceptions. He also endured a stretch of four straight games with a pick-six and earned a 73.0 rating -- his lowest as a starter.

But in 2012, Schaub enjoyed one of the best seasons of his career, throwing for 4,008 yards and guiding the Texans to a 12-4 mark. Along the way, he threw for 22 touchdowns, 12 interceptions and a 90.7 rating. It was the third time in four years that Schaub threw for more than 4,000 yards.

Overall, Schaub has gone 46-44 in his 10-year career, compared to 3-1 for Hoyer, who was brought in by the since-departed Joe Banner and Mike Lombardi.

The Browns, who own the No. 4 overall pick, and the Texans, who have the No. 1 overall selection, could both end up drafting quarterbacks with their top picks.

New Texans coach Bill O'Brien also coached Hoyer in New England and likes him. It wouldn't be surprising for O'Brien to make a pitch for the Cleveland native, but coach Mike Pettine has praised Hoyer since taking the job and it's unknown if the Browns would part with him.

But one thing is certain: Shanahan knows how to bring out the best in Schaub. In his three seasons under Shanahan, his ratings were 87.2, 92.7 and 98.6.