The singer, who is currently promoting his new Unconditional Love Songs album, was quizzed about ex-wife Katie Price's wedding to Alex Reid and custody of his children.
"I couldn't care less [about the wedding]. I'm so sorry. I'm not being bitter. I understand that I have to be asked these questions. It is news," he said. "I don't complain about it."
During the interview, Burley showed Andre footage of Price's former lover Dwight Yorke speaking out against Andre's relationship with his son Harvey.
Responding to the clip, the I'm A Celebrity... star said: "The greatest respect, but has he seen Harvey since that interview? The bottom line is that I love that child. I see that child. A nice little thank you would be nice. I asked to adopt him because I love that child, not to be disrespectful. He's in my life and calls me dad."
When the Sky News presenter asked how he would feel if Reid wanted to adopt his children, Andre reacted angrily.
"No-one is going to take away my kids," he said. "I will fight to the death for that. Sorry, I didn't expect that. Nobody is going to take my kids away from me. I will die for those children."
When Burley pursued with the line of questioning, he added: "It is not going to happen. I will tell you now, I will go to court... I don't want to talk about this."
The host attempted to swiftly change the subject to Andre's upcoming live tour, but a tearful Andre said that he did not want to continue with the interview.