Oakland doesn’t sign its players to multiyear deals, or so the story goes.

That hasn’t always been true, of course. The team has inked many of its key contributors to multiyear deals during the Billy Beane era, some just through their arbitration years, a few longer. And the A’s still engage their players in discussions about multiyear deals: Oakland approached shortstop Marcus Semien about a contract of up to five years this past winter, according to sources, and the team briefly talked to outfielder Khris Davis about a multiyear deal.

If the A’s signed Semien — who’s from El Cerrito and Cal — to something akin to what the White Sox did with shortstop Tim Anderson, who got a six-year, $25 million deal last offseason, it would take him past arbitration; Semien is due to be a free agent after the 2020 season.

Semien, who missed three months of the season with a wrist fracture, would be open to revisiting the multiyear talks. “I don’t see why not,” he said. “I want to make sure it’s worth doing, of course. Every player wants to make sure they’re doing what’s right for them and their family. But ever since I broke my wrist, nothing’s happening and I’m hitting below .200, so I don’t know. We haven’t talked since the spring.”

Vice president of baseball operations Billy Beane said Sunday that the A’s goal is to commit to a full rebuilding and, aided by a new stadium, eventually to be able to sign the team’s top players long-term — beyond arbitration — which is something Oakland has almost never done except in the cases of Eric Chavez and Mark Ellis.

“I think really what’s been missing here the last 20 years is keeping these players,” Beane said Sunday. “The frustration isn’t in the fact that we’ve had success. The frustration is that after success we haven’t kept them, and it’s just a fact, and we need to change that narrative by virtue of creating a good team and then ultimately committed to keeping them around, so people, when they buy a ticket, know that the team’s going to be there for a few years.”

Manager Bob Melvin is, naturally, enthusiastic about the direction the team is taking and the commitment to Oakland and finding a stadium in the city, building something solid.

“It’s refreshing to hear now that the narrative has changed here,” he said, adding that he knows Beane and general manager David Forst feel the same way. “We can change the way we do business around here, and I think the timing is great because we do have a lot of younger guys we do feel will be part of our future.”

The club hasn’t had a ton of luck, though, when signing its players to multiyear deals — in a majority of instances, injuries almost immediately happened. Chavez, Ellis, Bobby Crosby, Brett Anderson and Sean Doolittle are among those who spent time on the disabled list after signing multiyear deals, and Coco Crisp spent extensive time out of action after receiving a multiyear extension.

Doolittle and Crisp are the only players the A’s have signed to multiyear deals off their roster in the past six years, but the practice used to be much more common.

In 2011, Trevor Cahill signed a five-year deal, Anderson got a four-year contract the year before that, and Kurt Suzuki a four-year deal in 2010. In 2007, Nick Swisher signed a five-year deal, Ellis signed a three-year deal in 2006, and Dan Haren a four-year contract in 2005. Crosby got five years that same year, and in 2004, Oakland signed Chavez to a six-year, $66 million deal, still the largest in team history.

Susan Slusser is a San Francisco Chronicle staff writer. Email: sslusser@sfchronicle.com Twitter: @susanslusser