Williams' name has already surfaced with regard to Washington, and D-backs manager Kirk Gibson was asked Friday how he thought Williams would do as a manager.
"I think he'd be great," Gibson said. "He's prepared, he was obviously a good player, we've worked closely together since I've been the manager. He's got a good mind for it. I know he managed in the Fall League last year. He was very good at that as well. I know he had one interview with Colorado last year, and hopefully he'll get an opportunity to represent his thoughts and his plan this offseason."
Williams declined to comment on any specific managerial opening, but has said in the past that he would love to one day manage in the big leagues.
The Rockies interview was Williams' first, but he impressed the Colorado front office.
"Matty was Matty," Rockies general manager Dan O'Dowd said last November. "He was prepared, organized with his thoughts, paid attention to detail and he was passionate. He came across so clear in what he wanted to do. There's no doubt in my mind he's going to be a big league manager real soon."
In addition to managing in the Arizona Fall League last year, Williams briefly managed Arizona's Double-A Mobile team in 2007 after manager Brett Butler had to miss the final two months due to illness.
Williams was Arizona's first-base coach in 2010, but switched to third in 2011 during Gibson's first full year as manager.
"He's a fierce competitor, understands the game, he breaks it down, tireless worker, believes in heavy preparation, never gives in," Gibson said.
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.