The D-backs dismissed third-base coach Chip Hale and first-base coach Lorenzo Bundy on Monday and a FOXsports.com report said the D-backs were considering Williams for one of the spots.
"If they're considering me, I'd love to sit down and talk to them about it to see what options there might be there," Williams said, adding that they have not yet spoken.
D-backs manager A.J. Hinch said he did not want to discuss who may or may not be candidates for the position, but did say, "Matt has done a lot of good things in this game."
Williams has played a variety of roles within the D-backs' organization since he retired as a player in 2003. Currently he is a minority owner of the team and holds the title of special assistant to president and CEO Derrick Hall. He also broadcasts select games on both radio and television for the club.
D-backs general manager Josh Byrnes said the team is currently compiling a list of candidates.
In 2007, Williams managed the organization's Double-A Mobile team for the season's final two months after manager Brett Butler suffered a stroke.
"I've had the opportunity to work with some of this talent on a temporary basis and enjoyed it," said Williams.
Current D-backs such as outfielder Justin Upton and pitcher Max Scherzer were on that Double-A team.
Williams was a member of the inaugural D-backs team in 1998 and finished his 17-year playing career with the organization.
"I'm most comfortable in uniform on the field working with players," Williams said.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.