The last time Teoscar Hernández gazed out at the crowd at Dodger Stadium, the veteran outfielder almost broke down crying.

“I just want to say thank you,” Hernández said during the Dodgers’ World Series celebration at Chavez Ravine last Friday, having played a crucial role in the club’s first full-season championship since 1988.

Hernández then stopped, getting choked up with emotion. Before him, more than 40,000 fans began roaring in appreciation.

“I play this game to win,” Hernández continued, the serenading from the stands amplifying with every word. “And the Dodgers gave me the opportunity to come here, so I could help this organization, this team, these people, this city, win a championship. You guys made this dream come true. Thank you for making me a world champion.”

If not for Hernández, the Dodgers might not have had a championship to celebrate.

After signing a one-year, $23.5-million contract last offseason, he became one of the most important pieces in the Dodgers’ indomitable lineup, racking up 33 home runs and 99 RBIs in the regular season, plus a number of key hits — including his score-tying, two-run double in Game 5 of the World Series — during their postseason run to a title.

A week later, Hernández is back on the free-agent market, where he will be a more coveted commodity than last winter following his resurgent performance. And as the Dodgers evaluate their plans for this winter, whether or not they retain him could be a key determinant to the entire offseason.

As general manager Brandon Gomes acknowledged Wednesday, the club’s biggest focus on offense this winter is bolstering the outfield. That was true even before Gomes announced that right fielder Mookie Betts likely will move back to the infield next year. Now, it’s a glaring need with few obvious solutions.

The Dodgers don’t have an established everyday outfielder on their roster, with only platoon bats such as Andy Pages, Chris Taylor and James Outman under club control for next season.

The team could shift utility man Tommy Edman, who received most of his playing time this October at shortstop, to an everyday role in center field. The Dodgers’ top prospect, catcher Dalton Rushing, also can provide depth after finishing this season playing left field in triple A.

But this season, much of the Dodgers’ offensive success revolved around the consistent, clutch hitting by Hernández.

And — barring a run at free-agent superstar Juan Soto, 26 — it could be a struggle for the Dodgers to find appealing alternatives if they don’t bring back Hernández.

“Teo was a huge part of what we accomplished this year,” Gomes said Wednesday at Major League Baseball’s general manager meetings. “On the field, you could see it very clearly. Huge impact in the clubhouse with younger guys, his energy. So we’ll have conversations with Teo and his group ASAP.”

The good news for the Dodgers: Hernández’s desire is to remain in Los Angeles on a long-term contract. The 32-year-old Dominican Republic native relished his first season with the organization, in which he earned his second All-Star selection, became the club’s first Home Run Derby winner, and posted the second-highest batting average (.272) and on-base-plus-slugging percentage (.840) of his nine-year career.

In the clubhouse, he carved out an important leadership role, forming bonds with everyone from Shohei Ohtani (Hernández was among the first Dodgers to strike a relationship with the $700-million star in spring training) to younger faces like Pages (whom Hernández took under his wing during the rookie’s solid season).

And after playing for three teams over the last three seasons, Hernández is hopeful of finding stability in the Southland, telling reporters after Friday’s stadium celebration that his “hopes are really high” for re-signing with the Dodgers.

“The Dodgers are the priority, obviously,” he said. “I’m going to do everything in my power to come back.”

The question is whether the Dodgers feel as strongly, and if they’ll be willing to reward him with the three-year contract he is believed to be seeking.

In the short term, retaining Hernández seems like a no-brainer for the Dodgers.

He could move to right field, his strongest defensive position. He could maintain continuity in the lineup, where he formed a potent top four with Ohtani, Betts and Freddie Freeman. And he could help preserve the clubhouse culture that fueled the Dodgers’ October run.

If the team has any plans to “run it back” with the same roster core — something manager Dave Roberts and a couple of players already hinted they hope to see — re-signing Hernández would be a top priority.

However, the Dodgers front office, which declined to engage in extension talks with Hernandez’s agents during the season, also accounts for long-term risk in personnel evaluations. And giving a 32-year-old player who annually has one of the league’s higher strikeout rates a lucrative, three-year deal — Hernández is projected to receive between $60 million and $70 million on the open market — would represent a break from their typical operating procedure.

Yet, the risk of losing Hernández also should factor into their decision-making.

The only better outfielder in this free-agent class is Soto. He is expected to trigger a bidding war between the New York Yankees and New York Mets that might push his price tag upward of $700 million, a staggering amount that even the deep-pocketed Dodgers, who signed Ohtani to a heavily-deferred deal last winter, might be wary of spending again.

The rest of the market is headlined by the likes of Anthony Santander, Tyler O’Neill and Jurickson Profar, with other veterans such as Alex Verdugo, Jesse Winker, Randal Grichuk and Tommy Pham also available as lower-cost options.

The Dodgers could explore the trade market too — they still have a highly touted farm system and might be tempted to deal second baseman Gavin Lux now that Betts is set to return to the infield — but there aren’t likely to be many impact bats available there, either.

It’s why, as the Dodgers try to map out their winter plans, Hernández looms as one of the offseason’s most important linchpins. And if they fail to re-sign him, they will have to defend their championship without one of the players who was most responsible for helping them win it.