In this April 30, 2019, file photo, Boston Red Sox's Mookie Betts smiles as he crosses home plate on his solo home run off Oakland Athletics starting pitcher Aaron Brooks in the first inning of a baseball game at Fenway Park in Boston. Betts and the Red Sox agreed Friday, Jan. 10, 2020, to a $27 million contract, the largest one-year salary for an arbitration-eligible player. Credit: Charles Krupa | AP

BOSTON — The Boston Red Sox say the turmoil in the manager’s office isn’t a reason to give up on this season and trade outfielder Mookie Betts.

“The goal remains to be competitive always,” Chief Baseball Officer Chaim Bloom said this week after Alex Cora was ousted, leaving the Red Sox without a manager with less than a month before spring training. “2020 is important. So are 2021, 2022 and beyond.”

The 2018 AL MVP, Betts has been the subject of trade rumors this winter because he is in the last year of team control before he is eligible to become a free agent. The two sides avoided arbitration and agreed to a one-year, $27 million contract for this season.

“He’s the biggest person for our team, or one of the biggest,” shortstop Xander Bogaerts said on Thursday at a Fenway Park availability before the annual Boston Baseball Writers Awards Dinner. “We have a lot of veterans in this clubhouse to make another run. We’ve been through the good and we’ve been through the bad, and we’re still here. We should have a great year again this year.”

Red Sox infielder Michael Chavis also said he was excited nothing came of the trade rumors.

“Mookie did a lot for me,” he said. “I’m very thankful he’s back.”

Although the Red Sox are one of baseball’s biggest-spending clubs, owner John Henry has said he wants the team to get under the $208 million threshold for the collective bargaining tax. Going under the threshold for one year would lower the tax rate in future seasons.

Henry later clarified that resetting the team’s luxury tax penalties is a goal, not a mandate. But the only way to do that would be to unload a high-salary player; Betts would be the most valuable trade bait but also difficult to give up — unless they were looking at 2020 as a rebuilding year.

That’s not the case, the team’s brass insisted.

“We have high expectations in 2020,” Red Sox president Sam Kennedy said. “We fell short last year, [but] … we’re better than an 84 win club. We think we have a team that’s built to compete in the American League East.”

Cora left on Tuesday, a day after Manfred suspended Astros manager AJ Hinch and general manager Jeff Luhnow for a year for failing to stop an elaborate, illegal sign-stealing scheme that involved banging on trash can lids to relay pitch calls to the batter during the 2017 season, when the Astros won the World Series.

Cora was a bench coach on that team, and he reportedly implemented a similar scheme after taking over as Red Sox manager in 2018. In his first year on the Boston bench, the club won a franchise-record 108 regular-season games and the World Series.

Major League Baseball withheld Cora’s punishment for his role in the Astros shenanigans until it had finished the investigation into Boston. But the Red Sox did not wait, saying on Tuesday that Cora could not effectively lead the team; on Thursday, the New York Mets made Carlos Beltrán, a player on the 2017 Astros, the third manager to lose his job in the scandal.

Cora admitted wrongdoing, apologized and went willingly, the Red Sox said. They would not comment on the terms of any financial settlement over the two years remaining on his contract.

“It’s hard, especially the day I got the news,” said Bogaerts, who learned of Cora’s departure when he picked up his phone after a workout and saw a teammate had posted a frowning emoji. “It will be someone that we all miss a lot.”

Chavis, a rookie last year who spent 95 games in the majors and the rest in Triple-A, said he didn’t see anything untoward while he was with the Red Sox.

“You hate to see somebody lose his job,” Chavis said. “I would have loved to play for Alex again, but that’s out of my control.”