Princess Diana’s brother Earl Spencer insinuated that he’d already spoken to his nephews, Prince William and Prince Harry, about the bombshell claims he makes about her death in his upcoming book.

Spencer told the BBC’s Laura Kuenssberg in his interview Friday, “I don’t like to talk about what I’ve been speaking about to William and Harry, but this will not be a surprise to them.”

“I will tell you that these words will not be a surprise to them,” he insisted.

Spencer’s comments echo what an insider told Page Six last week about Harry’s reaction to his uncle’s claims about his mom’s death in his upcoming book, “Swan Song: Diana, My Sister.”

“It didn’t come as a shock,” a source in the know told us.

We’re told the two actually discussed the book during Harry’s visit to the Spencer ancestral estate, Althorp, back in July when he brought his wife, Meghan Markle, and their kids — Princess Lilibet, 5, and Prince Archie, 7 — to see his mother’s burial site.

In Spencer’s highly anticipated new book, he alleges King Charles III told him that Diana would be forgotten “soon enough” in a horrific phone call following her death in 1997.

“He unleashed down the phone what I have always taken to be his pent-up contempt for Diana, and his horror that the world was so bowled over by her death,” Spencer claimed, per an excerpt obtained by the Daily Mail. “’Rest assured,’” he hissed, ‘we’ll forget her soon enough!’”

Spencer said he was in disbelief at the time and hung up the phone.

He also alleged that Charles “sounded giddily elated — like a lottery winner” after his ex-wife died.

“Looking back now, I suspect the prince’s first reaction must have been to think more of how this event might free him to marry the woman he loved, rather than appreciating the loss of one he did not,” Spencer mused, referring to now-Queen Camilla, whom Charles wed in 2005.

But 77-year-old Charles — who had a famously tumultuous marriage to Diana from 1981 until they split in 1992, and finalized their divorce four years later — has hit back at Spencer’s claims.

A rep for Buckingham Palace told Page Six, “While we do not comment on books as a matter of principle, His Majesty is mindful that the pain of fraternal grief can cloud reason, affect judgment and colour memory in ways others do not recognise, even many years after such a loss.”

Spencer, 62, doubled down on his claims in his interview with Kuenssberg, insisting he was “telling the truth.”

“I can tell you here and now, those are exactly the words he said,” he stressed.

“I was hyper alert to what he was saying and those are precisely the words that he said and I promise that to you now. Genuinely, that is what he said. I don’t hear him saying he didn’t say that.”

“Swan Song: Diana, My Sister” is out Tuesday in both the UK and the US. Spencer also told the BBC that he sees parallels between how his late sister was treated and with how Harry, 42, and Markle, 45, are treated by the public.

“If you look at an article in a tabloid about Diana or the couple that you’re mentioning, Harry and Meghan, they can be really, really unpleasant,” Spencer said.

“I think it would be really beholden on people to learn from Diana’s example,” he continued, referencing her tragic death following a car crash in Paris at age 36.