Schaub, a two-time Pro Bowler, saw his 2013 season go south as he only threw 10 touchdowns to go with 14 interceptions. He eventually lost his starting job to Case Keenum after four straight games with a pick-six.
According to the report, Schaub would be a good fit with the Brown because he would reunite with his former offensive coordinator Kyle Shanahan.
"Schaub 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.