Simon, 53, joined Lauren at an ultrasound recently when they discovered the sex of their unborn baby. According to the New York Daily News, the "over the moon" father-to-be couldn't resist telling his friends.
An insider confirmed the news to US Weekly, adding, "They've known for a while!"
Simon recently spoke to The Times about attending the scan — although he didn't reveal anything about the baby's sex.
"I went to see a scan today and it is just surreal," he told the newspaper on Monday. "You literally see this thing which is now alive moving around. I feel very paternal right now."
The TV star is very much looking forward to becoming a father when American socialite Lauren, 36, welcomes the new arrival in 2014.
Speaking to BBC Breakfast, he said, "I am good with kids because I like kids. I really do like them and I listen to them.
"Once I got used to it (becoming a father) I did get excited. I think I will be a good dad, so I'm excited."
There is one thing Simon won't be dealing with, however — dirty nappies. "I'm not doing that, 100 per cent absolutely not going near that," he said. Asked if he would delegate that job to someone else, he replied, "Of course."
Mum-of-one Lauren is thought to be around four months pregnant with Simon's baby. She reached a divorce settlement with her husband of ten years last month.
Property mogul Andrew Silverman filed for divorce shortly after the news broke of his wife's infidelity with his close friend.
The former couple have come to an agreement to share joint custody of their seven-year-old son.
Simon - whose fortune is estimated at $368million - was cited as a "co-respondent" in the court papers for adultery.