The tapes are reportedly not publicly available, but segments from at least eight different appearances on the shock jock's show, spanning from 1997 to 2008, were published this week by Buzzfeed.
ABC News reached out to both Trump's campaign and a spokesperson for the radio show, and neither immediately returned requests for comment.
In them, Trump talks on a wide variety of topics largely unrelated to his businesses or current political ambitions, focusing more on ranking women by their attractiveness and his sexual attraction to them.
"She was crazy, but these are minor details," he said of the late royal.
Playing Up Beauty in Beauty Pageants
According to the Buzzfeed report, in 1997, the year after he took a financial stake in the competition, Trump said that he would work to have the "bathing suits to be smaller and the heels to be higher."
In 2005, when promoting the pageant on Stern's show, Trump said, "If you're looking for a rocket scientist, don't tune in tonight, but if you're looking for a really beautiful woman, you should watch," according to the Buzzfeed report.
His Own Attractiveness
In a separate 2008 interview, according to Buzzfeed, Trump said that women throw themselves at him, even though he had been married to his third wife Melania for three years at that point.
"They’ll walk up, and they’ll flip their top, and they’ll flip their panties," he said of his alleged unnamed fans.
During a 2005 appearance on the show, Trump said that he planned to have kids with his new wife, but "I mean, I won't do anything to take care of them. I'll supply funds and she'll take care of the kids. It's not like I'm going to be walking the kids down Central Park."
The couple's son, Barron, was born the following year.