The source also claimed that Caprice took a liking to a decorative bowl at the palace, and the Duke let her take it home.
"She spotted a bowl she liked and asked Andrew if she could steal it and post it to her mum. She claims that he let her, and her mum loved it!"
Andrew's efforts to impress the 48-year-old model didn't count for much, with the source telling the Sun: "She did think it a bit strange that he wanted to hang out as, from her side, there was no chance of a snog — she didn't fancy him."
Andrew isn't the only member of the Royal Family to express an interest in Caprice, a model who has previously been named the world's sexiest woman and who was once Prince Harry's teenage crush.
A friend told the Sun that the Duke let Caprice know that Harry was jealous of their relationship.
"He told her that his nephew, Prince Harry, was very intrigued by their friendship," the friend said.
"Apparently Harry had Caprice's calendar on his bedroom wall at Eton, and Harry was grilling Andrew over Christmas pudding at Sandringham about his crush."
Although Caprice and Andrew's relationship was short-lived, she did introduce him to her masseuse, Denise Martell.
After she treated him, the pair began a relationship that would last 10 years.