Smith, who was cut by Tennessee last week, played for the Chiefs and Romeo Crennel during the 2010 season. He has played for Crennel in 2007 and 2008 while in Cleveland.
If signed Smith would join the defensive tackle rotation. If he is not signed before the Sept. 9 season opener the Chiefs could add Smith to their roster with a non-guaranteed, one-year contract.
In other AFC West notes:
The NFL is changing its injured reserve rules. A player put on the injured reserve after Tuesday can now be brought back during the season when healthy. Previously, when a player went on the injured reserve, they were ineligible to come back during that season. This new rules allows teams to add depth while shelving a player for a while. One such candidate is San Diego receiver Vincent Brown, who will likely miss about half the season with a broken ankle.