Linley is the son of the Queen's only sister and her husband Lord Snowdon.
Queen Elizabeth II smiles as she arrives at Tweedbank Station on September 9, 2015 in Tweedbank, Scotland. Photo / Getty
In the same excerpt of John's autobiography, John wrote about how Richard Gere and Sylvester Stallone almost got into a fistfight over Princess Diana after she'd separated from Prince Charles.
He also explained how he had a falling out with Diana before reconciling before her death.
He said the pair disagreed over a book of photographs that Diana was supposed to have written the forward for.
"Then she got cold feet. I think Buckingham Palace didn't like the idea of a member of the Royal Family having anything to do with a book that featured shots of naked guys with towels draped around them."
John said. "So, at the last moment, Diana withdrew her foreword. She said she had no idea of the book's contents, which just wasn't true: Gianni had shown her the whole thing and she had said she loved it.
"I wrote back to her, calling her out, telling her how much money she had cost the AIDS Foundation, reminding her that she had seen the book."
Elton John's biography Me will officially be published on October 15.