NEW YORK — Running away with the AL East and heading into what they hope will be a deep playoff run this October, the New York Yankees desperately need to add a starting pitcher by the July 31 trade deadline.

Meanwhile, a scant eight miles across town, the New York Mets, closer to last place than first in the NL East and headed for their eighth sub-.500 season in the last 10, are eagerly seeking to unload a starting pitcher, and a good one at that.

And yet, it is less likely that the Mets would trade Zack Wheeler to the Yankees than it is that the two teams will meet in the 2019 World Series, the odds of which some books set at 225-to-1.

Throughout their 57-year history of mostly uneasy co-existence, the Yankees and Mets have cooperated on a trade precisely 15 times, beginning with the sale of 35-year-old right-handed pitcher Bob Friend from the Yankees to the Mets in 1966. Friend, a 16-year veteran, went 5-8 in 22 starts for the Mets and retired at the end of the season.

View photos Zack Wheeler is likely to be traded by the Mets next week, but not to their crosstown rivals, the Yankees. (Getty Images) More

In the interim, you could count the number of impactful deals between the intercity rivals on Three-Finger Brown’s hand. In 2001, the Yankees swapped David Justice for Robin Ventura. In 2003, the Mets shipped Armando Benitez to the Bronx for three Yankee “prospects,’’ none of whom amounted to much. And in 2004, they exchanged relievers: Mike Stanton of the Yankees going to Flushing in exchange for Felix Heredia.

Although Wheeler is almost certain not to be a Met next Thursday, it is just as certain he will not be included in the fourth “major’’ Yankees-Mets trade. That is, if there ever is one.

“We’d be crazy to put ourselves in the position of having them win with one of our guys,’’ a member of the Mets front office told Yahoo Sports this week when asked about the possibility of Wheeler going to the Yankees.

The source — who like everyone contacted for this story requested anonymity because of the sensitive nature of the relationship between the two clubs — went on to say that if the Mets received two comparable offers and one of them came from the Yankees, the Mets would reflexively reject the Yankees and accept the other offer.

“The Yankees would have to offer more than any other team for us to deal with them,’’ the source said.

It amounts to a “Yankee Premium’’ imposed because of the lingering resentments and hostilities between the two clubs. According to members of both organizations, most of that hostility flows from Flushing toward the Bronx these days, but it was not always thus.

“When Fred [Wilpon] and Nelson Doubleday were running the Mets, I think George was the over-paranoid one,’’ said a member of the Yankees hierarchy. “He always wanted to fight them for the back page. But later on, Fred and George became good friends and a lot of that went away.’’

But with Fred’s son, Jeff, now in charge of the Mets operations as their COO, relations have cooled back to the Cold War proportions of the '70s and '80s.

Most recently, the Yankees twice thought they had traded for outfielder Jay Bruce from the Mets in 2017, only to have then-GM Sandy Alderson pull the deal back at the last minute after talking to Mets ownership.

That same year, when a deal that would have sent Neil Walker to the Yankees fell through due to medical issues, there was finger-pointing in both directions.

New Mets GM Brodie Van Wagenen has said he would be open to dealing with the Yankees, but considering the reception of the Mets toward a possible Wheeler-to-the-Bronx deal, that seems highly unlikely.

“It doesn’t have to be this way,’’ said a Yankees official. “There’s more than enough room for two teams in this town.’’

Said another member of the Yankees front office: “It’s their issue. It’s not our issue.’’

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