The TV mogul is expecting his first child with Lauren Silverman early next year.
News of their relationship was the subject of scandal over the summer as Lauren was still married to businessman Andrew Silverman when she became pregnant.
According to TMZ, the socialite signed a divorce settlement agreeing that Simon would not go near the former couple’s seven-year-old son.
If that stipulation is not adhered to, Lauren will reportedly be forced to pay Andrew a $50,000 penalty.
TMZ claims to have obtained a copy of the agreement, “which also provides that if Lauren violates the Simon stay-away clause three times, she loses all contact with her son, Adam, until a court deals with the violations".
The stay-away clause is reportedly in place until January 2015.
Lauren and Andrew allegedly agreed Adam would not call anyone other than the two of them “mother” or “father”. In exchange Andrew apparently acknowledged he would not “trash Simon” to their son.
Andrew is said to be paying $3,000 a month in child support as part of the deal.
The parties have not commented publicly on their divorce settlement.
Simon recently opened up about impending fatherhood, but admitted he has no plans to quit smoking when his baby boy arrives.
"There are a lot of boring things that happen when you have a baby. [You have to get rid of] sharp edges, cigarettes, alcohol… then there's [baby-proofing] the toilet. But I'll have a smoking room!" he laughed to People.
The X Factor judge is also turning parenthood into somewhat of a competition.
"I was just texting with [One Direction's] Louis Tomlinson last night because his mom is pregnant and is going to have the baby the same time as Lauren. So it's like, who is going to go first? I think I am going to win,'" he laughed.