The Red Sox are picking a strange time to pinch pennies.

After holding baseball’s highest payroll the past two years and ranking in the top four since 2015, Boston’s front office is publicly acknowledging it may not be able to afford to keep outfielder Mookie Betts — laying the groundwork for a potential trade of the 26-year-old MVP — in order to fall below the luxury tax threshold, which the franchise has paid the past two years.

“We need to be under the CBT,” John Henry, the team’s controlling owner, said Friday.

The need for a four-time All-Star, and five-tool star just entering his prime, may not be as strong.

Betts was drafted by the Red Sox in 2011 and led the team to a franchise-best 108-win campaign last season, while becoming the first player in Major League history to win an MVP, Gold Glove, batting title, Silver Slugger and World Series in the same year. Betts, who agreed to a one-year, $20 million deal to avoid arbitration this season, has one year left on his rookie contact, and is likely headed to arbitration in the offseason.

But a once-unthinkable trade of their best player could come before he plays another game in Boston. J.D. Martinez, 32, has the ability to opt out of the final three years of his contract in November, but he will be owed more than $62 million if he plays out the remainder of his deal.

Red Sox president Sam Kennedy was pessimistic that the team could keep both lineup fixtures.

“There is a way, but obviously it will be difficult given the nature of the agreements and the contracts we have in place,” Kennedy said Monday at Fenway Park. “We have a very targeted and strategic plan that we’re building now. … It is going to be a challenging offseason, but we’re ready to attack it head-on and do everything we can to put a competitive team out there not just for next year but 2021, 2022.”

The comments from Kennedy and Henry come as the Red Sox are searching to replace general manager Dave Dombrowski, who was fired at the end of this season.

Even if Martinez is back, he doesn’t expect Betts to be alongside him very long.

“I think everyone knows we don’t think they’re going to be able to afford Mookie,” Martinez said Sunday. “It’s one of those things. It’s kind of hard to have three guys making $30 million on your team. He deserves it. He’s earned it.”

It was less than a year ago that the Red Sox signed journeyman pitcher Nathan Eovaldi to a four-year deal worth nearly $68 million. Then, in March, Chris Sale signed a five-year extension worth $145 million. Through 2022, the team will be paying David Price for the final years of the $217 million deal he signed to come to Boston.

Now, the cost of keeping perhaps the second-best position player in the sport could be considered too much. With Betts appearing set to hit free agency next winter, he could top Bryce Harper’s $330 million deal.

“I think it speaks to Mookie’s confidence and how special of a player he is,” Kennedy said of Betts’ desire to become a free agent. “He really does love it here. He told me he loves it here. … You can see with the joy and energy and enthusiasm in which he approaches playing baseball at Fenway Park — the fans love him.

“We absolutely love Mookie Betts as a player, as a person. We’ve gotten to know his family. You hope that he’s a guy that is here for the long term.”