In a statement, her law firm, Cohen Clair Lans Greifer & Thorpe, said: "We are working to resolve this situation in a fair and reasonable way that protects the best interests of our client and her son."
Cowell has remained tight-lipped about the story and refused to comment directly when he appeared at a press conference in Los Angeles ahead of the new series of the US version of the talent show.
"I've haven't read the newspapers," the 53-year-old music mogul joked, as he was questioned about the reports.
Asked if his schedule would be affected by being a father, he replied: "I really haven't read the newspapers. Did I miss anything?"
He added: "Unfortunately, I have to keep this, for the moment, private. It's just one of those things. Thank you very much anyway."
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 Silverman after her marriage hit the rocks.
- PAA