The deal, which includes a partial guarantee on the salary, would deliver Chalmers back to a Grizzlies franchise with which he had success in the 2015-16 season, before missing all of last season rehabilitating a ruptured Achilles tendon.
Chalmers, 31, gets a chance to make the Grizzlies' roster as a third point guard, with a head coach, David Fizdale, who worked with him for seven seasons as an assistant with the Miami Heat.
Chalmers, who played on two NBA championship teams in Miami, is part of Memphis basketball lore. His off-balance buzzer-beater to send the 2008 NCAA championship game into overtime will forever be remembered in Memphis. Chalmers, 31, would go on to win the Final Four's Most Outstanding Player award for his part in Kansas' victory over the University of Memphis.
Two years ago, Chalmers averaged 10.8 points in 55 games for the Grizzlies.