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Tampa bench coach Dave Martinez is out of the running for Toronto's manager spot. ((Steve Nesius/Associated Press))

The Toronto Blue Jays have started paring down their list of managerial candidates, with Rob Thomson and Dave Martinez among those told they are out of the running.

Internal applicants Luis Rivera, the manager at double-A New Hampshire, and Sal Fasano, manager of single-A Lansing, have also been eliminated from the search, according to multiple sources with knowledge of the process.

Thomson, the New York Yankees third base coach from Sarnia, Ont., and Martinez, the former Montreal Expo and Blue Jay who is now the Tampa Bay Rays bench coach, were both considered strong potential contenders for the post.

Still very much in the running are Boston Red Sox bench coach DeMarlo Hale and Cleveland Indians first base coach Sandy Alomar Jr., the sources said.

The status of Red Sox pitching coach John Farrell, Los Angeles Angels bench coach Ron Roenicke, San Diego Padres first base coach Rick Renteria, Philadelphia Phillies bench coach Pete Mackanin, Blue Jays third base coach Brian Butterfield, and bench coach Nick Leyva is less clear.

Still, the fact that some candidates are already being eliminated from the process indicates that general manager Alex Anthopoulos is making some headway in his exhaustive search for the retired Cito Gaston's replacement.

Anthopoulos has been working in a tight shroud of secrecy for fear of tipping his hand with so many other teams also searching for a new manager, refusing to offer any specific updates on his progress.

Vacancies filled

While the Chicago Cubs' hiring of Mike Quade, Eric Wedge's selection by the Seattle Mariners and Tony La Russa's return to the St. Louis Cardinals in recent days have filled some of the vacancies, Florida, Pittsburgh, Milwaukee and the Mets still have openings.

Former Blue Jays managers John Gibbons and Carlos Tosca have been linked to the Pirates as have Dale Sveum, Jeff Banister, Bobby Valentine and Ken Macha, who was fired by the Brewers.

Milwaukee is reportedly looking at Bob Melvin, Joey Cora and Pat Listach, among others.

MLB.com reports that Bo Porter is high on the Florida Marlins' list, although there is speculation they may take a run at Ryne Sandberg now that the Cubs have hired Quade.

The Blue Jays have been aiming to have a new manager in place shortly after the World Series ends so they can close the book on their thorough process and focus on off-season business.

Anthopoulos and his staff have been, in the words of the GM after the season ended, "consumed" by the search, engaging in multiple conversations with prospective candidates and conducting comprehensive background checks.

Hale, a 49-year-old from Chicago, served as Red Sox manager Terry Francona's bench coach last season after four years as the team's third base coach. He's won multiple manager of the year awards while working in the minors in the Red Sox system.

Alomar, the older brother of former Blue Jays second baseman Roberto Alomar, is a former all-star catcher with Cleveland who just finished his first season as first base coach with the Indians. The 44-year-old spent the previous two years as the big-league catching instructor for the Mets after retiring at the end of the 2007 season.