The 25-year-old's mother Sharon, 58, famously does not get on with her former X Factor co-star and Kelly got involved by letting rip about the singer.
She told British OK! magazine: 'I will be the first one to admit that my mother didn't play her cards right when it came to Dannii Minogue.
'But trust me when I say Dannii is the devil, the best thing to happen to Dannii's career was that my mother hated her.'
Osbourne also opened up about her battle with drugs and drink.
She said: 'I was born an addict and I'll always be an addict but I've learnt to live with it.
'There are different levels of addiction, whether it be drugs, spending money, overeating or painting your nails 17 times day.'
The reality TV star added: 'If I had one drink, it would turn into 20 and it would turn into drugs... which would turn into puking, which would turn into fighting.'