The Girls Aloud singer's first official book, 'Through My Eyes', is available to buy from next Thursday (30 September) -- the same day as Minogue's 'My Story' hits bookstores.
A source close to Kylie's sister told The Sun: "It's a massive blow. Cheryl's so popular and bound to outsell her. It's like anything you can do, I can do better."
The source was also quoted saying: "Dannii's already missed a lot of 'X Factor' glory because of baby Ethan. She should be coming back as a triumphant yummy mummy - instead she's coming back as second fiddle. It could be coincidence but it rains on Dannii's parade horribly."
Currently Cole would appear to be winning the sales fight. Her book is No. 5 in Amazon's pre-release chart, while Minogue is at No. 8. Both books have been slashed in price.
Although Dannii's camp fear her biography will be overshadowed by Cole's, it has already caused plenty of headlines in the Daily Mail with its revelations about her conflict with Sharon Osbourne -- the judge Cole replaced in 2008. In response, Osbourne's daughter Kelly fired off a Twitter tirade at the Australian calling her "the devil" and "a poor middle-aged victim".