Chargers general manager Tom Telesco is familiar with Mathews. Telesco was in the Colts' front office when Mathews was a seventh-round pick in 2010. Over four years in Indianapolis, Mathews played in 52 games and had 51 tackles and 1 1-2 sacks.
Mathews was signed in the offseason by the Houston Texans, but then released over the weekend.
The Chargers were encouraged that ailing defensive linemen Lawrence Guy, another former Colt brought in by Telesco, and defensive tackle Sean Lissemore practiced. Also, linebacker Manti Te'o was working after missing the final two preseason game with a left foot injury.
The Chargers open the season next Monday night against the Cardinals.