Larry Beinfest, Jerry DiPoto and Ben Cherington among rumored names.

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OAKLAND, Calif. – While the Mariners play out the final 28 games of the season, the clock is ticking on the personal and flexible deadline that team president Kevin Mather has imposed on himself to find a replacement for general manager Jack Zduriencik.

Mather fired Zduriencik on Aug. 28 in Chicago. Since then, he’s begun the process of adding to a list of candidates he’d already had in mind and then winnowing the list down to four or five finalists.

When discussing what he was looking for in candidates, Mather spoke in broad generalities.

“With a GM, the second word is manager,” he said. “It’s too big a job for one person to know everything about it. I need a manager who knows that he needs help and is wise enough to listen to all the departments. And at the end of the day he makes the decisions.”

And ….

“The important part, for me, is finding someone who’s smart enough to know what he doesn’t know, and will bring in people to help in this area or that area,” he said. “I’m looking for someone who is smart enough to check all the data points.’’

Beyond those comments, Mather believes that the core group of players returning next season and beyond can compete for a postseason spot as was expected this season.

While he determines his finalists for the job, here’s a look at some of the more prominent and mentioned names that fit his criteria and are likely on his list of possibilities.

Larry Beinfest

Former Marlins president of baseball operations/GM

Beinfest was fired by Marlins owner Jeffrey Loria in 2013 after 12 seasons with the Marlins. During his tenure in south Florida, Beinfest dealt with the constant shifting of payrolls from season to season. His crowning moment came in 2003 when the Marlins defeated the Yankees in the World Series behind right-hander Josh Beckett and the acquisitions of Pudge Rodriguez and Juan Pierre. He has some history with the Mariners. He came to the organization in 1989 as a player development and scouting assistant in the Mariners’ minor-league operations staff.

Since being fired, Beinfest has been under contract with the Marlins and has spent the last two seasons with his family. It officially ends on Oct. 31.

The good: Besides signing Rodriguez and trading for Pierre midseason in the World Series run, Beinfest also replaced manager Jeff Torborg with veteran Jack McKeon in May, traded for closer Ugueth Urbina and third baseman Jeff Conine to replace the injured Mike Lowell. Key moves to the title run. … The team drafted Jose Fernandez and talented outfielder Christian Yelich with first-round picks and selected Giancarlo Stanton with a second-round pick.

The bad: Needing to shed payroll, Beinfest traded Miguel Cabrera and Dontrelle Willis to the Detroit Tigers for then-top prospects Cameron Maybin and Andrew Miller and four other minor-league players. No matter what Maybin and Miller would become, he traded away a Hall of Fame player … There were several first-round failures in his tenure.

Ben Cherington

Former Red Sox general manager

It seemed unlikely Cherington would be available going into the season. But the Red Sox and their lack of quality pitching flopped this season. With president and ally Larry Lucchino fired, Cherington watched as the team brought in Dave Dombrowski as Lucchino’s replacement, effectively stripping him of his power. A protégé and sidekick of former general manager Theo Epstein, Cherington replaced his mentor and found immediate success, fixing the Bobby Valentine mess of 2012 by hiring manager John Farrell and revamping a roster that allowed the Red Sox to win the 2013 World Series. He’s served as an international scouting director, director of amateur scouting and director of player development during his early years in the organization.

The good: The revamping of the 2013 roster was aided significantly by a trade that sent the bloated contracts of Adrian Gonzalez, Carl Crawford and Josh Beckett to the Dodgers. … The decision to bring in Farrell was a perfect fit for a team sick of Valentine’s baseless bluster. … ESPN’s Keith Law rates Boston as the top minor-league system in all of baseball with a slew of hitting prospects led by infielders Rafael Devers and Yoan Moncada. The Sox have also developed shortstop Xander Bogaerts and outfielder Mookie Betts into solid contributors.

The bad: The roster setup for the 2015 season was bad from the start. Cherington spent $183 million on the acquisitions of Pablo Sandoval and Hanley Ramirez. The attempt to have Ramirez play left field failed. The team also started the season with Rick Porcello and Joe Kelly as its best starting pitchers and a collection of fodder after that. The hope was to outscore teams early and trade for help pitching midseason. Neither happened.

Jerry Dipoto

Former Angels general manager/ Red Sox consultant

If there was a favorite of the group, it might be Dipoto. He was a finalist when the team hired Zduriencik after the 2008 season. He knows the American League West and the Mariners, having spent 3½ seasons as the general manager of the Angels. Dipoto resigned from his position midseason after repeated disagreements with manager Mike Scioscia and the lack of backing from Angels owner Arte Moreno in the standoff. The Red Sox hired him as a consultant for the remaining few months of the season. Dipoto has knowledge of both analytics and scouting. The push for analytics in lineups and roster decisions and day-to-day preparation was something that Scioscia and Dipoto reportedly clashed on.

The good: Even though it was an easy decision to make, Dipoto was able to lock up Mike Trout to a 6-year, $144.5 million contract, which appears to be a bargain. … The Angels did win a league-high 98 games last season before bowing out to the Royals in the playoffs. The two biggest signings of his tenure — Albert Pujols at 10 years, $240 million and Josh Hamilton at 6 years, $125 million — weren’t really his based on reports. Moreno superseded Dipoto for those deals, saddling the organization with those two burdensome contracts. … Dipoto did trade Mark Trumbo for lefties Hector Santiago and Tyler Skaggs. Santiago was an all-star this season. He’s also added young pitchers Andrew Heaney and Nick Tropeano to provide depth.

The bad: Dipoto signed C.J. Wilson to a $75 million contract. And while Wilson has been somewhat reliable in taking the ball every five days, he is no longer the effective starter that earned him the contract. The failure to bring in a top-level starter hurt the Angels in the playoffs last season. Meanwhile, gambles on free-agent pitchers like Joe Blanton and Ryan Madson and trading for broken-down Tommy Hanson never bore fruit.

Kenny Williams

White Sox executive vice president

In 12 seasons as Sox GM, his teams won a division title in 2005 and 2008 and a World Series title in 2005. His teams finished above .500 in nine seasons.

The good: Before his World Series season, Williams signed outfielder Jermaine Dye, infielder Tadahito Iguchi, catcher A.J. Pierzynski and right-hander Orlando Hernandez — all key contributors that season. The season before he acquired Freddy Garcia, who was vital in the World Series run. Following the World Series, he signed Paul Konerko — the team’s heart and soul — to an extension.

The bad: Williams has taken some gambles that haven’t helped. Claiming Alex Rios and his bloated contract off of waivers didn’t help. He traded for Jake Peavy in 2009 when he was hurt and had to wait for the right-hander to recover from a torn lat muscle. He gave up Gio Gonzalez to acquire Nick Swisher before the 2008 season and then traded Swisher later that season for three players — the best being Wilson Betemit.