"I was born to be a dad," the X Factor judge told his ex and long-term friend, Terri Seymour, on Extra.
He also said that he was reduced to tears when he laid eyes on his son for the first time, just seconds after he was born and was surprised by the immediate love he had for him.
He said:"'I actually said to Lauren beforehand, "What if I like the dogs more than him?" and she said, "You're gonna be absolutely fine," and then literally within seconds of him being born, I got it!"
Simon, whose baby news with girlfriend Lauren Silverman came as a big surprise, seems to be a natural. Since Lauren gave birth to baby Eric – who the couple named after Simon's late father Eric Selig Phillip Cowell – he has posted several touching photographs of the family.
And there may be additions in the future, according to the music mogul. When asked if he would have more children, the 54-year-old replied: "I wouldn't rule [it] out".
He continued, mentioning his two treasured Yorkshire Terriers: "Well, I got 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."
Since Eric's arrival in New York's Lennox Hill Hospital on 14 February, the couple have enjoyed some down time and have even managed to take their newborn to relax on Miami beach.
The trio will head to London Wednesday, when Simon's mum Julie will meet her beloved grandson for the first time.
Speaking about his mum, Simon joked that her phone is now constantly engaged. "I think she's told the whole village ... she's really excited," said the proud new dad.