NEW YORK — They are two of the two biggest stars in baseball’s greatest rivalry, and when they stand on the field Friday for the opening day ceremonies at Yankee Stadium, it could be their final seasons with the New York Yankees and Boston Red Sox.

All-Stars Aaron Judge and Xander Bogaerts could each be free agents after the 2022 season.

They’d given their teams a Friday deadline to reach an agreement on a long-term contract.

Judge remains hopeful, with his agent still in negotiations with the Yankees about an extension.

Bogaerts said Thursday that contract talks are over with the Red Sox.

“It just didn’t work out,’’ said Bogaerts, who rejected the Red Sox’s offer. “That’s behind us now. I can’t really think about that right now. It is what it is.’’

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The Yankees realize what Judge, a three-time All-Star outfielder, means to the organization, and haven’t tried to hide how badly they want him to remain in a Yankee uniform the rest of his career.

The Red Sox feel just as passionate towards Bogaerts, a three-time All-Star who has already played on two World Series championship teams and assisted on recruiting his possible successor, Trevor Story, to the organization.

Now, they will be facing each other on opening day for perhaps the final time.

The Yankees are willing to make Judge one of the highest-paid outfielders in baseball, surpassing George Springer’s six-year, $150 million contract with the Toronto Blue Jays, but a deal approaching Mike Trout’s 10-year, $360 million extension is unrealistic.

Judge, who turns 30 in three weeks, is three years older than Trout was when he signed his extension. The Yankees, according to a person with direct knowledge of the negotiations, are willing to offer a six- or seven-year extension, cognizant of Judge’s past injuries, limiting him to 63% of their games from 2018-2020.

Yankees first baseman Anthony Rizzo was in a similar situation a year ago with the Chicago Cubs when he was eligible for free agency at the season’s conclusion. The two sides never came close to reaching an agreement, and Rizzo was traded to the Yankees at the trade deadline.

“I have talked to him a little bit about it,’’ Rizzo said. “At the end of the day, it’s about what is going to make him and Sammy [Judge’s wife] happy, and what his value is, what his worth is. It’s extremely high in this game. He’s a legitimate MVP candidate every single year, and he knows that. …

“When it comes to the business side, there’s no secret. You see Freddie Freeman isn’t on the Braves anymore. There’s no loyalty in the game. When you separate that, and the business side, and take your heart out of it, that’s the tough part.’’

While Judge will naturally be disappointed if an extension isn’t completed, just like Bogaerts, but Yankees manager Aaron Boone is convinced it won’t have any effect on him. Judge hit .406 this spring with four homers and a 1.347 OPS in 11 games.

“I don’t think it impacts him at all,’’ Boone said. “I know where his focus is on. It’s on his team, his teammates and trying to win a championship.

“Whether he signs an extension or doesn’t, but I don’t think it matters at all. I know where his head is, what he’s focused on, and what he’s prepared to lead us to do.’’

Bogaerts’ situation is different than Judge. He could simply stay put with three years and $60 million remaining on his original six-year, $120 million contract extension.

Yet, considering the market for star shortstops, with Corey Seager receiving a 10-year, $325 million contract this winter with the Texas Rangers, and the extensions by Mets shortstop Francisco Lindor [10 years, $341 million] and Padres shortstop Fernando Tatis [14 years, $340 million] a year ago. Carlos Correa became the highest-paid shortstop on an annual average salary basis with his three-year, $105.3 million contract with the Minnesota Twins, including two opt-out years.

“I can’t do nothing about it right now,’’ Bogaerts said. “I’ve got a season coming up in front of me, and I don’t want to put any of our teammates in that type of distraction. They don’t deserve it. We had time to get something done. It didn’t work out.

“We’ll see how it goes from there.’’

The irony of Bogaerts’ contract situation is that he might have hurt his own bargaining position after the lockout by persuading Story to come to Boston, where he’ll play second base. If Bogaerts departs, the Red Sox simply will move Story back to shortstop.

“We want Bogey to be here for a long time,’’ Red Sox GM Chaim Bloom told reporters in spring training. “We’d love to have both of them here for a long time.’’

The Yankees say the same thing and are hopeful that Jose Ramirez’s team-friendly five-year, $124 million contract extension with the Cleveland Guardians could play a factor. Ramirez finished in the top six of the AL MVP race in four of the past five years, with a WAR behind only Mookie Betts and Mike Trout.

The Yankees don’t pretend that Judge should sign a similar deal, but it reflected how much Ramirez wanted to stay in Cleveland. The stark difference, as well, is that Cleveland threatened to trade Ramirez to San Diego if he didn’t reach an agreement. The Yankees vow that Judge will stay all season.

If no deal is reached by 1:07 p.m. ET Friday, they are scheduled to meet in an arbitration hearing later this month. Judge filed for $21 million; the Yankees at $17 million.

It just might turn out to be the closest they’ll ever get again in contract talks.

“He’s really good in this game, how he handles everything,’’ Rizzo said. “I’ve admired him from afar. For years, I heard nothing but good things about him. I come over last year and meet him, and he’s the total package.

“What he brings to this organization is something I haven’t seen before.’’

This article originally appeared on USA TODAY: Yankees-Red Sox: Aaron Judge, Xander Bogaerts could become free agents