The music mogul is hopeful that his first child will follow in his footsteps.
"He has to take over for me," Simon said, "I’ve put him in training. He’s down at the shows, he has the earplugs in. I would absolutely love it if he could do what I do."
Simon told The Sun newspaper: “If he gravitates towards academics, then fine – I would encourage him but I have a feeling he’s gonna be more like me.
“I’m not gonna lie, I’d love him to one day say, ‘Can I work for you and learn how to do it.’
“That would make me feel incredible — and then you have a legacy.”
Last year, Simon said that Eric was already showing off his music knowledge backstage filming The X Factor.
Speaking ahead of the previous series, Simon said: "At the moment he seems to know more about music than I do! If I say to him, ‘Can you tell me the lyrics to this record’ he will literally repeat the entire song.
"So when he watches all these movies, like Trolls, which has an amazing soundtrack by Justin Timberlake, he knows every word, who the original artist is, and if I tell him the song he just repeats it. I think he’ll probably end up doing what I am doing."
Simon continued: "He’s quite shy, when I am filming and I put the microphone in front of him, I’ve got to really push him to say something. But it’s amazing how quickly he’s got what I do.
"I used to ask him what daddy does for work and he’d say ‘You press buttons’, that’s BGT.
"Then Louis said to him today, ‘What does daddy do’ and he just said, ‘He talks into a microphone!’. That’s what he thinks I do! He really has got good taste in music though and is very interesting to watch because when we get new records come in from our artists, I watch him when we play the record.
"If he’s interested then it’s a really good chance it’ll be a hit. He’s got fantastic instincts."
The X Factor and Britain's Got Talent air on ITV.