Red Sox would love to retain World Series hero Nathan Eovaldi

Nathan Eovaldi (right), with David Price, was a key member of the World Series champions.jim davis/Globe staff/Globe Staff

Update: On Dec. 6, Nathan Eovaldi and the Red Sox reached an agreement on a new deal.

When Red Sox manager Alex Cora looks back at the World Series it’s at the only game his team lost.

He believes the 3-2, 18-inning setback against the Los Angeles Dodgers in Game 3 led to the Sox winning the final two games of the Series to claim the championship.

Specifically, it was the six innings and 97 pitches Nathan Eovaldi threw in relief that changed the course of the series. That the righthander allowed a walkoff homer by Max Muncy didn’t matter given how determined the Sox were to win the Series afterward.

“That’s the moment. That was the moment,” Cora said Monday night at the Emerson Colonial Theater before the premiere of MLB’s documentary on the Red Sox. “For him to go out there and pitch the way he did, it was unreal. That was such a performance.”

Which raises the question: Why is Eovaldi still a free agent?

The Red Sox need a reliable starting pitcher to fill out their rotation and the 28-year-old Eovaldi is just that. He was 3-3 with a 3.33 earned run average in 12 games after being obtained from Tampa Bay in July, then had a 1.61 ERA in six postseason games.

“We have expressed that we do have interest in bringing Nathan back,” president of baseball operations Dave Dombrowski said. “We’ve talked to him. But so have a lot of other people talked to him. There’s a lot of interest in him.

“He’s a guy that we’d love to keep. We’ve talked about that. But he’s got a lot of choices at this time.”

Eovaldi, who is from the Houston suburb of Alvin, has interest from the Astros and several other teams. With Chris Sale and Rick Porcello entering their free-agent seasons, retaining Eovaldi is particularly important to the Sox.

His proven ability to pitch out of the bullpen in the postseason also matters for a team that hopes to repeat as champions.

“We’ll see what the future has,” Cora said. “He’s a game-changer. We know the stuff he has. He got better with time. He went though the process of mixing up his pitches and attacking guys in different spots. Hopefully it happens and he’s part of this.”

Craig Kimbrel, Joe Kelly, and Drew Pomeranz also are free agents.

“I would think that [with] every one of them, I’ve got a feel of what’s taken place,” Dombrowski said. “Some are more of a priority for us to try and re-sign than others.”

Whether it’s by retaining Kimbrel and Kelly or looking elsewhere, the Sox appear much more likely to complete their bullpen via free agency than trade.

“I don’t know what the demand will be as far as clubs are concerned. But there’s a lot of guys out there. That’s something we would be more apt to pursue,” Dombrowski said.

Pedroia on track

Brock Holt, the only player who attended the premiere, said he has been keeping in close touch with Dustin Pedroia and that the second baseman is doing well with his left knee.

“From everything that I’ve heard from him he says he feels good,” Holt said. “I don’t know the exact regimen he’s on but every time I talk to him he says it feels fine. He would tell me if it’s not . . . he’s been very positive.”

Dombrowski said the next test for Pedroia would be starting a running program in early January.

Pedroia had surgery in October 2017 and a follow-up procedure in July. He played only three games last season.

Staff changes?

Several Red Sox front office staffers were granted permission to interview with other teams and could leave the organization. “I’m not sure if it will happen or not but the possibility exists,” Dombrowski said . . . The Red Sox selected a new manager for Triple A Pawtucket but Dombrowski would not reveal his choice . . . Although the Red Sox need a closer, they were not involved in the trade talks that led to Seattle Mariners All-Star Edwin Diaz being traded to the New York Mets. As part of the seven-player deal, the Mets agreed to take Robinson Cano and pay $100 million of the $120 million he is owed through 2023. “That situation wasn’t a fit for us,” Dombrowski said . . . Principal owner John Henry said after the World Series the team would look to extend Dombrowski’s contract. The 62-year-old Dombrowski offered no comment on the status of those talks other than to say he enjoyed his work and planned to continue in the foreseeable future