Simon, 54, intends to introduce four-month-old Eric to the entertainment industry from an early age.
He revealed: "I'm going to be in the UK a lot for the foreseeable future and we've got a lot on with the X Factor auditions - I might even take Eric with me to some of the recordings."
When asked how he would react if his son wanted a singing career instead of becoming a businessman, Simon said: "If Eric wants to try out being a singer, I would be OK with that. I certainly won't stop him.
"But I'll tell him straight if he can't do it. Admittedly, I might not be quite as blunt as I am with some of the contestants."