He recently found out he fathered a child with an ex-girlfriend following a paternity test.
But he says he's not planning to be involved in raising the boy, now three-years-old.
'I'm not ready to have another son brought into my life,' he says in a new documentary. 'While it sounds nasty, I've got my family.
'I don't want anything to do with him, though financially I'll do as best I can to help out. It's not up for discussion.'
Mark, 37, and Kerry, 28, have Heidi, 18 months, and Max, 8 months.
He also has six-year-old daughter Keeley from a previous relationship.
Kerry Katona: 12 Months Of Mayhem airs on MTV One on Sunday at 9pm.