SAN DIEGO — As the Giants end another disappointing season and dive into what promises to be a turbulent winter, they finally need to address one of their most critical questions in perhaps decades, which has no easy answer:

What are they going to do with pitcher Madison Bumgarner, one of the greatest players to wear their uniform and one of the greatest postseason pitchers in the game’s history?

In an interview before the Giants’ game against the Padres on Wednesday night, Bumgarner made his intentions clear.

“I’d like to be here,” he said. “I guess it’s a little early to talk about finishing my career, but I’d like to be here my whole career. But that’s not 100 percent in my control.”

The thought of Bumgarner wearing another uniform might be sacrilegious to the faithful, but with one option year left on the contract he signed when he was 22, the Giants need to address the possibility — and Bumgarner knows it.

“I know there are a lot of different ways they can go with it,” he said. “I don’t know anything more than you do. I’ll kind of see what happens and what their plans are.”

The possibilities are all over the board.

The Giants could reward Bumgarner with a rich extension that a pitcher with his pedigree would seek when he reaches free agency for the first time. They could exercise his option for 2019 and let the season unfold, punting a decision until the July trade deadline or next offseason.

Or, they could accelerate their rebuild after a second consecutive losing season by trading the 29-year-old left-hander now for younger players, a direction to which teams in the Giants’ position historically have turned.

Bumgarner said he remains open to extension negotiations, but he and his representative have not heard from the club.

Team officials are thought to be weighing a boatload of variables, particularly their chances of competing for a title next year and Bumgarner’s relatively low 2019 salary ($12 million), versus the need to restock their farm system via trades and his expected performance as he moves into his 30s.

With one World Series ring in hand, Bumgarner signed a six-year, $35 million contract before the 2012 season. At the time, it was the largest ever given to a player who had not reached two years of major-league service. With his 2018 and 2019 options, the contract will have paid him roughly $70 million.

That made him significantly underpaid for a pitcher who helped the Giants win three World Series titles, including his historic performance in 2014. He threw five shutout innings of relief in Kansas City in Game 7 after going nine innings to win Game 5 three nights earlier.

The Giants can take heart in one thing: Bumgarner does not expect them to pay him more than he deserves to compensate him for all he did while earning relatively little.

“I don’t think you can expect somebody to pay you more than they think you’re worth just because of something like that,” he said. “At the same time, guys are looking to get paid what they think they’re worth compared to the market and how other players are getting paid.

“I signed that deal. They didn’t know if I was going to outperform it or underperform it, and I didn’t, either. I don’t think anybody could expect that. I don’t think that would be fair.”

Before the 2016 season, the Diamondbacks gave Zack Greinke a six-year, $206 million deal when he was 32. Bumgarner is expected to seek at least that, but he would enter free agency at a time when teams are devaluing starters and reluctant to risk that type of money on pitchers.

Bumgarner does not buy that, saying, “I don’t think starting pitching is any less important than it’s ever been,” he said. “I don’t think that will ever go away.”

He also remains skeptical that the market has changed, viewing last winter as an aberration as teams held back their spending to stay under the luxury-tax cap.

Bumgarner is not the pitcher he once was. Though he carries a healthy ERA (3.14) into Friday night’s start in St. Louis, he does not throw with the same velocity as he once did, and his peripherals — stats that teams view as more predictive — are trending in the wrong direction.

He is putting runners on base at the highest rate of his career, and his fielding-independent pitching (an adjusted ERA based solely on walks, strikeouts and home runs), is also at a career high in his second straight injury-shortened season.

The Giants must consider all of this ahead of their decision. His stature, history and doggedness on the mound certainly will play into it, too.

Bumgarner has two starts left in 2018. He is not viewing them as anything like a Giants swan song because of the possibility that he could be traded.

“I hadn’t really thought about it much,” he said. “I don’t want to make decisions for them. I’m not looking at it that way. I’m a one-day-at-a-time kind of guy.”

Henry Schulman is a San Francisco Chronicle staff writer. Email: hschulman@sfchronicle.com Twitter: @hankschulman