The music mogul told Extra that he had not ruled out having a brother or sister for son Eric, who was born on Valentine's Day
The 54-year-old said: "I wouldn't rule out (more children). Well, I got (Yorkshire terriers) Squiddly and Diddly, and I couldn't imagine Squiddly or just Diddly ... I had a brother when I was younger, so I kind of think it's cool to have two or three ... two."
Cowell said that he cried at his son's birth after dashing to New York from London - where he was filming Britain's Got Talent auditions - to be at girlfriend Lauren Silverman's side.
He admitted he felt some trepidation about becoming a father.
"I actually said to Lauren beforehand, 'What if I like the dogs more than him?', because I've never had a baby before, and she said, 'You're gonna be absolutely fine', and then literally within seconds of him being born, I got it," he said.
Interviewed by his ex-girlfriend Terri Seymour, the X Factor judge said of his dash to the US: "The phone rings at half past five in the morning, 'I'm about to give birth' (said Lauren), so we had to find a flight, which we did, and I got there with two hours to spare."
He told Extra that his mother Julie was "really excited" and "touched" that the couple had decided to name the baby Eric, after Simon's father.
"Lauren told her (about the name) and she was really touched by it, because we were going to call him Simon but we both thought, you know, this is not a good idea, so we decided on Eric.
"I look at him, Eric, and I think of my dad all the time, so it's a really good thing."
He said of life since the baby was born: "Lauren's actually been crying more than Eric, so I've had to put one of those pacifiers in her which she likes ... has to be fed every three hours, otherwise she gets a little bit grumpy, and Eric's absolutely fine!"