The encounter with reporters took place before Mr Trump entered the 2016 presidential race at that year's CPAC conservative conference.
"Nice guy, got a lot of problems coming up in my opinion, with the famous island with Jeffrey Epstein," Mr Trump said.
Later, a Bloomberg reporter asked Mr Trump what "problems" he thought Mr Clinton would face.
"I don't know, but that island was really a cesspool, there's no question about it, just ask Prince Andrew, he'll tell you about it, the island was an absolute cesspool," Mr Trump said.
Prince Andrew was a friend of Epstein and met him through Epstein's former girlfriend, Ghislaine Maxwell. Ms Maxwell was arrested last month and is awaiting trial for child sex trafficking tied to Epstein's sexual abuse of children.
Many of the abuses Epstein committed occurred on his private island, Little Saint James.
Virginia Roberts Giuffre, a woman who claims she was trafficked as a 17-year-old by Epstein and Ms Maxwell, claims she was sent to have sex with Prince Andrew on three occasions.
Prince Andrew has repeatedly denied any wrongdoing.
In a widely criticised interview with the BBC last fall, he said he'd never met the girl, but he remembers being at a pizza shop with his daughter on the day in question. A widely-circulated photo of Prince Andrew shows him standing in a room with his arm around the then-17-year-old Ms Giuffre. Ms Maxwell also appears in the photo.
Prince Andrew – eighth in line to the British throne – said he was willing to make himself available to US officials investigating the Epstein case, but has been accused of "stonewalling" and being otherwise uncooperative by US investigators.
The prince's legal team denies that he has been uncooperative and claimed instead that he was being treated poorly by US officials.