Coleman made 29 starts and appeared in 59 games over four seasons in Philadelphia, three of those under current Chiefs coach Andy Reid. He was released by the Vikings during the final round of cuts on Saturday after spending the offseason and training camp with them.
Mays had surgery to repair damage in his wrist that he sustained during a preseason game. The veteran linebacker, who has played in 61 games over the course of six seasons, was being counted on to start alongside Derrick Johnson in the middle of the Chiefs' defense.
Kansas City opens the regular season Sunday against Tennessee.