Ron Gardenhire. (AP Photo/Carlos Osorio, File)

Asked what traits he would look for in a future manager of the Nationals, General Manager Mike Rizzo listed several, including communication, in-game tactics and leadership. Rizzo also made a point to say the Nationals would cast a wider net for candidates and experience than the last search that settled on rookie manager Matt Williams.

And of the pool of available candidates, Dusty Baker and Ron Gardenhire rank near the top in accomplishments. Baker was a three-time National League Manager of the Year — 1993, 1997 and 2000 with the San Francisco Giants — but hasn’t managed since 2013 with the Cincinnati Reds. Gardenhire was the American League Manager of the Year in 2010 and won six AL Central titles before being fired in 2014 after 13 years at the helm of the Minnesota Twins.

Both want to get back into managing again and have interest in the Nationals managerial vacancy. It doesn’t appear there is any reciprocal interest in either yet, or if there will be.

“I would think Ron would definitely be interested in the Nats job,” said agent John Boggs, who represents Gardenhire. “It’s a very attractive job and city, and a good team. What’s not to like? For someone wanting to get back into managing, it’s a great opportunity.”

Baker was interested in the Nationals the last time the manager’s job was open before the 2014 season. He asked his agent to contact Rizzo then but didn’t hear back. The Nationals remain an attractive option.

“It’s a good team,” Baker said by telephone. “I’d be interested in them. But you gotta have some interest in return.”

Baker, 66, owns a .526 winning percentage over 20 seasons as a big league manager, and his 1,671 wins rank 17th all-time. He has made the playoffs with three different teams. Baker guided the Giants to the 2002 World Series, where they lost in seven games to the Angels. He left San Francisco and won a division title with the Cubs in 2003.

Baker has drawn criticism for overusing starting pitchers and over-reliance on outdated tactics, such as frequent sacrifice bunts. But wherever he has been, he has won, and he has managed players with reputations for having difficult personalities, from Barry Bonds to Jeff Kent to Brandon Phillips. In six years with the Reds, he reached the playoffs three times, losing in the first round each time.

Baker, who lives in California and is doing television analyst work for TBS during the playoffs, knows Williams well. He managed Williams in San Francisco, and Williams has often said Baker was a mentor for him. The last time Baker threw his hat into the ring for the Nationals managerial job, he knew Williams was a strong candidate already.

“I wasn’t really that interested in the job because I wanted him to get it,” Baker said. “I told Matt that. I knew he had the job. The reason I had my agent call was not to cut Matty out but to show people that I still wanted to manage. I told Matty that was the main reason I called. It isn’t the situation now.”

Baker hoped to reach out to Williams soon, once the sting of the firing dissipated. He said he felt bad for Williams, who dealt with speculation about his job status for months, and the injuries that beset the Nationals roster.

“It’s nothing against Matt or anything,” said Baker, who added he hoped Williams lands another job soon. “Once you kinda get behind the eight ball and then gotta play catch up and gets even tougher.”

Baker was reportedly on the Marlins’ radar, but he said he hasn’t been contacted by them. He wants to be back in a major league dugout and his health has improved since a mini-stroke in 2012. He hasn’t been employed or considered a serious candidate for openings since the Reds job, which he doesn’t understand.

“I didn’t fire myself and I can’t hire myself,” he said. “Nobody has ever told me and I don’t know if anybody ever will.”

Like Baker, Gardenhire has a wealth of experience. At 57, he was rejuvenated by the year away from the dugout and is “very open” to managing again, Boggs said. Gardenhire posted a 1,068-1039 record with the Twins, the third most wins in team history. He was known for his old-school approach and tactics, and ability to relate to players. Nationals center fielder Denard Span, an upcoming free agent and former Twin, often said Gardenhire was a good guy.

Gardenhire had four 90-loss seasons in a row before the Twins went with new-school Paul Molitor, a rookie manager. But in those final seasons, Gardenhire didn’t have the same talent to work with that Molitor had or the Nationals could offer.

Veterans skippers will prove more costly to the Nationals, who have been reluctant to pay top dollar for managers. Williams is owed $1 million in 2016, the remaining guaranteed year on his contract. So if the Nationals tab an experienced manager, they will have to pay.