Simon's confession comes amid reports that he and his partner Lauren Silverman made an emotional visit to the home of his mum Julie to introduce her to her grandson. The meeting took place earlier this week, and it was the first time that 88-year-old Julie had seen Eric.
"It was a lovely visit from Simon and Lauren, and Julie was thrilled, " a source told the Mirror.
"There were some very emotional moments when she got to hold and touch Eric, and his name is obviously very poignant for Julie as her husband Eric died in 1999."
In a 2009 interview, Julie admitted that Simon had told her he didn't want children and that she "couldn't talk him round". Friends said that holding Eric this week was the "final piece in the puzzle" for the proud new grandmother.
Earlier this month, Simon spoke about becoming a father for the first time, saying he felt he was "born to be a dad".
In an interview on Extra with his ex and long-term friend Terri Seymour, he also revealed that he was reduced to tears when he laid eyes on his son for the first time, and was overwhelmed by the immediate love he felt for him.
Simon's mother Julie Cowell has been introduced to the baby
"I actually said to Lauren beforehand, 'What if I like the dogs more then him?'," Simon admitted. "And she said, 'You're gonna be absolutely fine', and then literally within seconds of him being born, I got it."
Certainly Simon seems to be a natural. Since the arrival of Eric - who the couple named after Simon's late father Eric Selig Phillip Cowell - he has shared a number of touching photographs of the new family. And there might be more children to come in the future. "I wouldn't rule it out," the X Factor judge revealed.