The former X Factor judge shocked members of the audience with her remarks about Minogue.
Asked by Piers Morgan why she had quit the ITV1 competition, Osbourne replied: "Dannii Minogue.
"All Dannii wanted to do was f**k Simon Cowell. That’s why she’s on the show."
The star continued by criticising Minogue's cosmetic surgery and described her as a "mosquito you want to flick away".
Osbourne quit the X Factor in July 2008 after reportedly seeking a salary of £2 million for the fifth series.
"They offered £1.6 million but she ‘couldn’t bear to sit next to Dannii six more months’," a source told The Sun.