"I'm not doing that, 100 per cent absolutely not going near that," he told the show, and asked whether he would delegate to someone else, he replied: "Of course."
Cowell also hinted that he will not let his baby get in the way when it comes to getting his beauty sleep.
Warned by Harry Hill, who has written The X Factor musical, that he would feel exhausted from sleepless nights, he replied: "Can't I just get a nanny?"
Cowell, who is promoting new musical I Can't Sing, spoke as the new contestants on this year's Strictly Come Dancing were unveiled.
He said that he relished the ratings battle with his own show, The X Factor.
"It's a little bit of a battle. I like that because you can't always assume that you're going to beat the competition but it makes us work harder," he said.
"It's annoying when they beat us but in other years we beat them. We'll beat them (this year)."
Cowell said that he had banned the words "journey" and "dream" from The X Factor.
"I hate people saying 'you're going on a journey' because you're not going on a journey. You're on a talent show."
He told Daybreak that the baby will be at the premiere of the musical, about a young woman who lives in a caravan and finds fame on an X Factor-style show.
Asked whether he had changed since finding out he was going to become a father, Hill joked of Cowell: "He fancied a rusk earlier."
Cowell admitted that he hated musicals.
"We have had people approach us before about musicals but they always took it really seriously."
- PAA
