Cowell could be called to court after he was named as a "co-respondent" in Silverman's divorce papers by her husband Andrew, the New York Post said.
Andrew Silverman, a property magnate, had filed for divorce based on his wife's adultery despite New York state allowing no-fault divorces, which means Cowell could be called to court to give evidence, it was reported.
Cowell's mother is said to be "delighted" about the news that her son is to become a father for the first time.
Julie Cowell told The Sun: "I'm delighted. It's wonderful!"
According to the newspaper, the talent show judge fell for 36-year-old Lauren Silverman after her marriage hit the rocks.
Meanwhile, Mail Online has published photographs of Cowell and Lauren on a Caribbean holiday in January last year.
Andrew Silverman was also on the holiday and the trio are pictured relaxing on a luxury yacht.
Britain's Got Talent judge David Walliams tweeted about the news, saying: "Oh yeah, and @SimonCowell is doing a baby with a lady."
Adding: "For the record @SimonCowell and I tried to have a baby together for many years. But I just couldn't get pregnant."
Cowell's friend, former pop star Sinitta, tweeted more cryptically: "Something has just happened... half miracle, half nightmare! #WakeMeUpIWantToGetOff!!"
- PAA