The former rugby player - who now lives in Australia - claims he and his ex-partner, who have 21-month-old son Ethan together, continue to be friends despite struggling with their relationship breakdown.
Speaking on Australian breakfast show 'The Circle', he said: ''It's a massive struggle, but you know we're the best of friends and we have a massive mutual respect for one another.
''Just taking one day at a time.''
Kris, who now works as a model, admits his son has helped him deal with his problems.
He said: ''He's sensational. He just picks you up every single day. He's a blessing.''
Dannii is believed to have turned to her sister Kylie Minogue when she was struggling with the end of her relationship.
A source said recently: ''She's been understandably scared about splitting up, but Kylie reassured her that she was strong enough to go it alone and that her happiness should come first.
''And in doing so it seems she gave Dannii the confidence to make the break.''