Osbourne also claimed that the Australian popstar was attempting to bully Louis Walsh off the panel in the same way this year.
Speaking out on Minogue's row with Walsh on last Saturday's live show over the song choice for their contestants, she defended the 56-year-old Irishman.
"Louis is genuinely upset because he doesn't want people to think he is a bully," she told The Sun.
"It's the last thing he is but that’s what people think when Dannii’s sitting like a porcelain doll with big fat tears rolling down her cheeks.
"She didn't cry when JLS came knocking at her door to ask for the song, did she? Her tears were only on live TV."
Commenting on her departure from the reality show, she said: "I got physically sick with the stress and the pressure. Nothing is worth that. I went through so much hurt and that was the biggest factor in me leaving The X Factor.
"There's the perception [Dannii] is the sweetest little thing in the world but she's not. She's a woman of the world. She's got balls of steel.
"She was always up Simon’s a**e and trying to be teacher's pet. She was always at his side, like a little stray dog. Her eyes turned brown she had her head so far up his backside."
Osbourne also claimed that she attempted to mend the rift between her and Minogue, only to be snubbed by the Australian.
"I said to her, 'What do you want me to do to make this work? I will walk over hot coals, will that make this better?'" commented Osbourne.
"She just stared at me like an iceberg, she never said a word."