The 55-year-old Britain's Got Talent boss says he wants a brother or sister for their son Eric, who was born on Valentine's Day last year.
He told the Daily Star he 'wouldn't rule out' the idea of adopting.
The X Factor supremo said: "Myself and Lauren want to have more children of our own but we could adopt as well. I wouldn't rule out it happening. It's a good idea.
"I'm beginning to warm to the idea of adopting."
Since becoming a father, Simon says he has become 'softer' – be he says he won't spoil Eric.
He said: "I'm aware Eric could become a brat. I'm going to make sure we teach him manners and to not talk down to people. I'm terrible at discipline but that's all basic stuff."
Eric is heir to his dad's TV and music fortune – thought to be around £300million. But Simon insisted he will have him working from an early age.
He said: "I'll teach him the value of money. That's what my mum and dad did with me. When they paid for holidays we had to earn our own spending money.
Simon returned to TV at the weekend with Britain's Got Talent and pressed his Golden Buzzer for 26-year-old singer Calum Scott, who wowed the audience with his rendition of Dancing On My Own by Robyn.
Simon told him: "I've never ever in all the years that I've done this show, heard a guy with the talent you've got. The version was sensational."
More on Parentdish: 10 things adoptive parents wish their family and friends understood
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