The 41-year-old singer and fashion designer was being persuaded by Cowell, who is planning a massive shake-up of his ITV talent contest after ratings fell this year, reported Sun online.
But, Minogue has ruled herself out by signing for the rival Sky Living show. She will join fellow Australian and host Elle Macpherson and model Tyson Beckford in the search for catwalk talent.
However, Minogue had rejected a 1 million pounds offer to replace R&B star Kelly Rowland on this year's "X Factor".
"This is two fingers up to Cowell. She is definitely not going back to 'The X Factor' and can't wait to get working on Britain and Ireland's 'Next Top Model'. Dannii loves the fashion world and this show is perfect for her," a source said.