But they had a connection, one Mr. Trump was quick to note in the moments after his first address to Congress in February 2017. As he made his way out of the chamber, Mr. Trump paused to chat with the justice.

“Say hello to your boy,” Mr. Trump said. “Special guy.”

Mr. Trump was apparently referring to Justice Kennedy’s son, Justin. The younger Mr. Kennedy spent more than a decade at Deutsche Bank, eventually rising to become the bank’s global head of real estate capital markets, and he worked closely with Mr. Trump when he was a real estate developer, according to two people with knowledge of his role.

During Mr. Kennedy’s tenure, Deutsche Bank became Mr. Trump’s most important lender, dispensing well over $1 billion in loans to him for the renovation and construction of skyscrapers in New York and Chicago at a time other mainstream banks were wary of doing business with him because of his troubled business history.

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If the overtures to Justice Kennedy from the White House were subtle, the warnings from its allies were blunt. Last month, Senator Charles E. Grassley of Iowa, the Republican chairman of the Senate Judiciary Committee, went on Hugh Hewitt’s radio program to issue an urgent plea.

“My message to any one of the nine Supreme Court justices,” he said, was, “‘If you’re thinking about quitting this year, do it yesterday.’”

Mr. Grassley said speed was of the essence in light of the midterm elections in November. “If we have a Democrat Senate,” he said, “you’re never going to get the kind of people that are strict constructionists.”

Intermediaries pressed the point with Justice Kennedy privately, telling him that Donald F. McGahn II, Mr. Trump’s White House counsel, would in all probability leave after the midterms. Mr. McGahn has been a key architect of Mr. Trump’s successful efforts to appoint wave after wave of conservative judges, they said, and his absence would complicate a Supreme Court confirmation.