Ward was the D-backs' assistant hitting coach in 2013 before serving as hitting coach the past two seasons.
The D-backs have filled three spots on their coaching staff already this offseason, hiring Mike Butcher as pitching coach, Matt Williams as third base coach and Garvin Alston as bullpen coach.
Assistant hitting coach Mark Grace is a name to keep in mind as a possible replacement for Ward, but another could be Dodgers hitting coach Mark McGwire, who has a long history with D-backs chief baseball officer Tony La Russa.
La Russa was McGwire's first big league manager from 1986-95 with the A's and he also managed McGwire with the Cardinals from 1997-2001. La Russa hired McGwire to be the Cardinals' hitting coach in 2010.
When the Dodgers parted ways with manager Don Mattingly following the season, McGwire and the rest of the Dodgers coaching staff were told they were free to look for other jobs if they desired.
The Dodgers have yet to hire a manager and McGwire is not under contract for next season.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.