Manning started the first six games last season before suffering a season-ending injury to his right knee. He became an unrestricted free agent on Monday.
Manning was Chicago's second-round draft pick in 2006. He went to Houston as a free agent after five seasons with the Bears.
He started nine playoff games with the Bears and the Texans. The Bengals lost at Houston in the opening round of the playoffs in 2011 and 2012. They were beaten at home by San Diego last season, leaving them with no playoff victory since 1990 - tied for the sixth-longest streak of postseason futility in NFL history.
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