Those close to Sen. John McCain John Sidney McCainCindy McCain endorses Biden: He's only candidate 'who stands up for our values' Biden says Cindy McCain will endorse him Biden's six best bets in 2016 Trump states MORE (R-Ariz.) have told the White House that their plan for the Arizona Republican's eventual funeral is to have Vice President Pence attend — but not President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE, The New York Times reports.

The funeral is expected to take place at the Washington National Cathedral, according to the Times.

But Trump, with whom McCain has had a tempestuous relationship, is not expected to attend the service, at least not according to current planning, the Times reported.

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McCain was diagnosed with an aggressive form of brain cancer last year, and is undergoing treatment. Despite his illness, the senator has continued to visit with friends and field conference calls with his staff back in Washington.

Still, some of his associates have said that they want a "McCain person" appointed to fill his Senate seat in the event of the senator's death, according to the Times. Among the list of potential picks is McCain's wife, Cindy McCain.

McCain has also acknowledged that his upcoming memoir, "The Restless Wave: Good Times, Just Causes, Great Fights, and Other Appreciations," will be his last book.

That title, set to be released this month, reflects on his 2008 presidential campaign and the years that followed. It also includes an admission by the senator that he regrets not choosing former Connecticut Sen. Joseph Lieberman, a Democrat turned independent, to serve as his running mate.

In his book and an upcoming HBO documentary, McCain says that his decision not to pick Lieberman, his longtime friend, was "another mistake that I made." McCain instead chose former Alaska Gov. Sarah Palin (R) as his running mate.

He also recalls how his campaign advisers argued that picking Lieberman as his running mate would divide the Republican Party because of his political affiliations, according to the Times, which obtained a copy of the book.

"It was sound advice that I could reason for myself," McCain writes. "But my gut told me to ignore it and I wish I had."