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SCOTTSDALE, Ariz. — It’s a story that was never confirmed and never will be now that so many years have passed. But at some point in the late 1940s, Red Sox owner Tom Yawkey and Yankees owner Dan Topping supposedly agreed over drinks one night in Manhattan to swap Ted Williams for Joe DiMaggio.

The notion was that the lefthanded-hitting Williams would hit home run after home run into the short right field porch at Yankee Stadium and DiMaggio would wear out the left field wall at Fenway Park with his elegant righthanded swing.

Saner heads, and perhaps a few aspirins, prevailed in the morning light and no deal was struck.

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The Sox and Yankees have actually made 11 trades since 1950, most involving prospects who never panned out or older players on the way down.

The Sox erred grievously in sending future Cy Young Award winner Sparky Lyle to the Yankees in 1972 but none of the other trades were particularly consequential.

Former Red Sox assistant GM Jed Hoyer, now with the Cubs, said Theo Epstein was enamored with Yankees first baseman Nick Johnson early in his tenure but nothing came of it.

The last Sox-Yankees deal came in 2014 when Ben Cherington dumped Stephen Drew on the Yankees for Kelly Johnson at the trade deadline.

Now, in the spirit of Williams and DiMaggio, should the sides consider an actual blockbuster?

As the Sox seek avenues to trim their payroll, one clear path would be to trade Mookie Betts and wipe away the projected $28 million he is set to make via arbitration next season.

That would require a trading partner with the financial means to add Betts and the young, affordable talent to satisfy the Red Sox.

The Yankees fit those criteria. More importantly, new Red Sox chief baseball officer Chaim Bloom, speaking generally, isn’t opposed to talking to the Yankees about a deal.

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“I think it would be irresponsible to dismiss that,” he said Monday.

Chaim Bloom said he wouldn’t be opposed to making a deal with the Yankees.
Chaim Bloom said he wouldn’t be opposed to making a deal with the Yankees.Matt York/Associated Press

That required some follow-up on Tuesday.

“I think in general our job is to do what’s best for the Boston Red Sox,” Bloom said during a break at the GM Meetings. “There’s a lot of considerations that go into that in any conversation . . . Obviously I know the relationship between this organization and the Yankees is not like any other clubs.”

Yankees general manager Brian Cashman said he has gone years without discussing anything with his Red Sox counterparts. But he’s also not opposed to it.

“If we put a player up for our auction, what’s the best deal? If the best deal happens to reside in your division, take it to ownership for them to make the final call,” Cashman said. “I’m interested in the best deal for this franchise and this fan base. But I know there’s some emotional stuff involved and that’s why ownership would make the decision.”

Cashman said the best atmosphere for the rivals to make a trade would be when one of the teams is going for it and the other is rebuilding.

The Yankees are clearly in win-now mode. The Red Sox aren’t necessarily rebuilding, but they are clearly in a period of transition under Bloom that will focus more on the future than selling out for the present.

Could the Red Sox entertain the thought of moving Mookie Betts to New York?
Could the Red Sox entertain the thought of moving Mookie Betts to New York?John Tlumacki/Globe Staff

So how about this deal:

The Sox send Betts and lefthander Jay Groome to the Yankees for infielder Miguel Andujar, outfielder Clint Frazier, and righthanders Luis Gil and Mike King.

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This is a trade that helps and hurts both teams, which is the only way it works.

The Yankees get Betts to hit leadoff and play center field for a World Series contender — plus a year to convince him to sign a long-term deal. That opportunity has a lot of value.

They also get Groome, a former first-round pick from New Jersey who is coming off Tommy John surgery. So if Betts bolts after a year, at least they can wish on Groome.

The Sox get a cornerstone player in the 24-year-old Andujar, who was second in the American League Rookie of the Year voting in 2018. He’s a third baseman but could play first or second base for the Sox.

But Andujar is no sure thing. He’s coming off surgery to repair a torn shoulder labrum.

Frazier, a former first-round pick of the Indians, hasn’t fit in well for the Yankees since they acquired him in 2016. He gets a fresh start and plays right field for the Sox.

The Sox also get two good prospects in Gil and King. The latter is a Rhode Island native who played for Boston College.

The Yankees haven’t won the World Series since 2009. Betts can put them over the top. The Red Sox clear payroll space, add two affordable starters and two prospects.

Andujar is a lot to ask. But the Yankees won 103 games and scored 943 runs with him getting 47 at-bats last season. The Yankees wouldn’t miss Frazier and can live without Gil and King.

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I asked a neutral GM his thoughts. He wasn’t willing to go on the record in discussing players from other teams, but did think it over for a few seconds.

“It’s not crazy,” he said.

There you have it. And no drinks were required.


Peter Abraham can be reached at pabraham@globe.com. Follow him on Twitter @PeteAbe.