The Giants will make one of their most important franchise-shaping decisions in years when they hire someone to run baseball operations, and they’ve pledged an extensive nationwide search.

That means reaching far and wide to conduct interviews with officials from playoff teams and non-playoff teams and possibly inside the commissioner’s office.

CEO Larry Baer said there’s no rush to make a decision, realizing that getting it right is more important than when it gets done — the new boss, after all, will help determine the organization’s road map to its short- and long-term future.

Well, the Giants need not go far to find extremely qualified officials who would be perfect to fill the role, perfect to operate with the right blend of scouts and analytics (as Baer wants) and perfect to pull the Giants from the hole they’ve been in the past 2½ seasons.

The A’s are simply across the bay.

Known as a trend-setting organization that does more with less than other teams, the A’s often are at the forefront of roster-building and game-planning, and Billy Beane has at least two top lieutenants who’d greatly benefit the Giants.

General manager David Forst has been with the A’s for 19 years, most of it as Beane’s right-hand man, and we lost count of how many interviews the Harvard-educated Forst turned down because he wanted to keep his family in the Bay Area.

Three years ago, when Beane was promoted from GM to executive vice president of baseball operations, Forst was elevated from assistant GM to GM. As a result, no other team could interview him for a GM job because it would be a lateral move.

The Giants’ gig would be a promotion, and teams traditionally allow executives to be interviewed elsewhere if it’s for a higher position.

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Another possible candidate with the A’s is widely respected Billy Owens, an assistant GM (and director of player personnel) who’s a front-office heavyweight and reliable source for Beane on any transaction. Owens has his fingerprints all over the A’s roster.

He would give the Giants’ front office diversity as an African American and a local presence as a San Jose native. He plays a significant role in amateur, pro and international scouting and is well versed in analytics.

One intriguing scenario that would make sense is for the Giants to hire Forst to run baseball operations and for Forst to bring in Owens as the GM.

It would be a step up for both executives and suit what Baer desires, a pecking order similar to the model constructed by the Cubs’ Theo Epstein and Dodgers’ Andrew Friedman, who run their teams’ baseball operations departments while surrounding themselves with GM types.

The A’s, who had the majors’ fourth-best regular-season record and were eliminated in Wednesday’s wild-card game at Yankee Stadium, have Bay Area bragging rights — regarding player personnel, obviously not ballparks. Snagging a key exec or two from the A’s would be a coup for the Giants, not only by solidifying their front office but by stealing some of the A’s thunder as Oakland moves forward with a promising young roster.

Now, there’s a little wrinkle. A’s owner John Fisher once was in the Giants’ ownership group, an original investor when Peter Magowan and Co. bought the team in December 1992, and it’s not as if there’s a lovefest between the teams’ ownerships.

Remember the territorial-rights hullabaloo?

Over the years, Beane has supported his assistants’ pursuits of GM jobs in other organizations — J.P. Ricciardi, Paul DePodesta and Farhan Zaidi all got promotions elsewhere — but this is unusual because of the Giants-A’s dynamic.

Would Fisher approve a Giants request to interview Forst or Owens?

It would be inappropriate for Fisher to step in the way of any employee’s career advancement, and certainly it wouldn’t be appreciated by Major League Baseball, which heavily encourages clubs to permit such interviews.

Yes, the A’s denied Bob Melvin an interview with the Yankees for the managerial job before New York hired Aaron Boone in December, but that was the A’s right because Melvin would have interviewed for the same position he had in Oakland.

Speaking of Melvin, his contract expires after next season, and he’s expected to receive an extension soon. There is a precedent for managers to have opt-out clauses — Joe Maddon left the Rays while under contract to run the Cubs — and if Melvin includes one in his new deal … well, imagine this:

Melvin (a Giants catcher in the late ’80s) replacing Bruce Bochy as manager in 2020 and working for a front office led by Forst and Owens.

That might be too much for A’s fans to digest, but make no mistake: The A’s have what the Giants want, a constant stream of young players who are drafted or acquired and regularly contribute at the big-league level.

The Giants are considering candidates across the country, but they could find exactly what they need across the bay.

John Shea is The San Francisco Chronicle’s national baseball writer. Email: jshea@sfchronicle.com Twitter: @JohnSheaHey