Stephenson, 27, has started 21 games since being drafted in the third round by the Chiefs in 2012, and his inconsistent play during that time often left the team frustrated.
Stephenson started seven games in 2015. He began the season as the starting left tackle in part because the Chiefs believed that was his best position, but before the year was over, he also had taken some snaps at right tackle and guard.
Stephenson was suspended by the NFL for the season's first four games in 2014 because of a violation of the league's policy on performance-enhancing substances.
ESPN Chiefs reporter Adam Teicher contributed to this report.