Long-swirling rumors over the exact nature of Donald Trump’s relationship with Princess Diana came into sharp focus today, after it emerged that Trump claimed on a radio broadcast with Howard Stern days after her death that he could have had sex with her.

“Why do people think it’s egotistical of you to say you could’ve gotten with Lady Di?” Stern asked Trump in the interview. “You could’ve gotten her, right? You could’ve nailed her.”

Trump replied: “I think I could have.”

The interview took place in 1997, just weeks after Princess Diana and her boyfriend, Dodi Fayed, were killed when their car crashed in a Paris tunnel in September 1997 as it was being pursued by paparazzi photographers on motorbikes.

Trump made a similar declaration in a separate 2000 broadcast with Stern, adding, she was “crazy, but these are minor details.”

“Would you have slept with her?” Stern asked in the latter interview.

“Without even hesitation,” replied Trump.

Both interviews were unearthed by BuzzFeed, which reported that it had listened to hours of Trump’s appearances on Stern’s show to track down the comments.

In the earlier interview, Trump claimed to have received a “really nice” letter from Princess Diana thanking him for a favor he had done her. He declined to say what the favor was.

However, last month the British TV presenter Selina Scott, a friend of Diana’s, claimed in the Sunday Times that Trump “bombarded Diana at Kensington Palace with massive bouquets of flowers” and that the princess had said the businessman gave her “the creeps.”

She wrote: “As the roses and orchids piled up at her apartment, she became increasingly concerned about what she should do. It had begun to feel as if Trump was stalking her.”

The American political consultant Bob Beckel, who managed Walter Mondale’s presidential campaign, has also added fuel to this particular fire. He said on CNN that there was a “letter” from Trump to Diana and that there was “stuff on Trump” that was “almost worse” than on Bill Clinton.

BuzzFeed reports that when a female contributor to the Stern show interjected “He wishes he’d had the opportunity,” Trump, who had phoned in to discuss his personal list of the world’s top 10 most beautiful women, admitted: “There’s a truth to that.”

He added: “She was really beautiful and people don’t realise how beautiful she was. She was super-model beautiful, she had the height, she had the beauty, she had the skin, she had the whole thing.”