The 28-year-old Allen missed the final two games of the 2017 season, his second with the Texans, because of a concussion. He also is recovering from multiple ankle injuries and was placed on the PUP list in May.
The 6-foot-4, 306-pound Allen, a second-round pick (No. 44 overall) out of Illinois by the Kansas City Chiefs in the 2012 NFL Draft, started 26 games at guard and tackle over two seasons in Houston after signing a four-year contract as a free agent in 2016.
Head coach Bill O'Brien and the Texans are rebuilding their offensive line to protect second-year quarterback Deshaun Watson, having signed free agents Zach Fulton, Senio Kelemente and Seantrel Henderson.
Houston also drafted Martinas Rankin in the third round (No. 80 overall) out of Mississippi State, and also like the development of tackle Julie'n Davenport, drafted last year in the fourth round (No. 130 overall) out of Bucknell.