CHICAGO -- With Jim Leyland announcing his resignation Monday, there is now another team looking for a new manager besides the Cubs, who have talked to Dave Martinez, Rick Renteria, A.J. Hinch and Manny Acta.

The Tigers join the Cubs, Reds, Mariners and Nationals in the market for a new skipper. That may create some competition for the top candidates. There were reports that Theo Epstein, Cubs president of baseball operations, also wanted to interview Red Sox bench coach Torey Lovullo, 48, whom Boston manager John Farrell believes is ready for a promotion. Lovullo's name also was mentioned as a possible successor in Detroit.

"To me, he's a manager-in-waiting," Farrell told reporters Saturday in Boston prior to Game 6 of the American League Championship Series. "I think he's going to have opportunities until he ends up securing one of the jobs. But he's been integral to the success that we've had here. He's a great baseball mind. The conversations and the feedback and just the insights that he gives, he's going to be very good."

Lovullo and the Red Sox are prepping for the World Series, which begins Wednesday.

"I want to make sure it's not a distraction here," Lovullo told reporters in Boston. "This is my focus, this is where I'm at, I'm proud to be a Boston Red Sox. I understand how the association happens because of Theo's connection to the Red Sox and me being here when Theo was here."

Epstein hired Lovullo to manage the Red Sox's Triple-A Pawtucket team in 2010.

Martinez, 49, told the Tampa Bay Times his interview with the Cubs went "really well." The former Cubs outfielder met with Epstein, general manager Jed Hoyer and others in the front office last Thursday in Chicago.

"They said they'd get back to me soon," said Martinez, who has interviewed for manager jobs in the past with the Indians, Blue Jays and Astros. He's been Joe Maddon's bench coach with Tampa Bay the last six seasons.

Renteria, 51, managed four seasons in the Padres' Minor League system before joining the big league staff as a bench coach. He also managed Mexico in the World Baseball Classic. He played parts of five seasons with the Pirates, Mariners and Marlins, and has managed in the Marlins' and Padres' organizations.

Acta, 44, managed the Nationals and Indians, and was let go from both jobs. Hinch, 39, is now in the Padres' front office and involved with player development. He managed the D-backs for parts of the 2009-10 seasons.

Epstein has stressed that the Cubs' next manager will be a key part of the development of young prospects, such as Javier Baez, Kris Bryant, Jorge Soler and Albert Almora. Besides continuing to emphasize "the Cubs Way," the new manager also has to create a winning environment.

"It's hard to hire managers," Epstein said on Sept. 30, when Dale Sveum was dismissed after two seasons at the helm. "It's clear Dale did some very productive things in two years. It's clear that we're transitioning from a phase where we're just acquiring young talent, most of whom we haven't seen up here yet, to a phase where that talent will start to come up in the next few years."

Major League Baseball discourages teams from making announcements during the World Series, so the Cubs most likely will have a news conference at Wrigley Field any time soon to reveal the team's 53rd manager. The only deadline Epstein has set is to have someone in place by Nov. 11, when the General Manager Meetings are held.