The 53-year-old let the baby's gender slip as he spoke about his plans to ensure his child has a British accent during an interview with US presenter Ryan Seacrest.
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"I said to Lauren, 'What if I just play me on tape while the baby is sleeping so the baby can hear me and have a British accent," he said. "And his first words will be, 'You're absolutely useless!'"
Simon then hinted that he will marry New York socialite Lauren, who is due to give birth in February, telling Ryan, "I wouldn't expect Lauren to be a single mother."
The TV host also quizzed him on whether he plans to be in the delivery room for the birth of his firstborn. "Are you out of your mind?" Simon replied. "There are certain things you shouldn't see and that is one of them."
Earlier this month, Simon spoke of his joy after seeing a sonogram of his unborn baby.
"I went to see a scan today and it is just surreal," he told The Times. "You see this thing which is now alive moving around. So I am happy."
The X Factor mogul had previously ruled out becoming a father, but has since said he feels overcome by the prospect of fatherhood.
"The fact that it can happen at this time of my life is fantastic, maybe a miracle," the 53-year-old told the Mail Online.
"Once I heard the news about the baby… little bit of a shock, then I got used to it, and then I became incredibly paternal and protective and I feel very attached to the baby already."
Simon has stepped out with Lauren on a number of occasions since the news of her pregnancy broke. She reached a divorce settlement with her husband of ten years last month.
Andrew Silverman filed for divorce shortly after it was revealed that Lauren was expecting a baby with Simon, his close friend. The former couple have agreed to share joint custody of their seven-year-old son.
Simon - whose fortune is estimated at £225million - was cited as a "co-respondent" in the court papers for adultery.
Despite his considerable wealth, Simon has said his baby won't have everything handed to him on a plate.
The star plans to leave his money to charity because he does not believe in passing inheritance on from one generation to another.
"Your legacy has to be that, hopefully, you gave enough people an opportunity, so that hey could do well, and you gave them your time, taught them what you know," he said.