The X Factor boss and music mogul appeared at a press conference in Los Angeles ahead of the new series of the US version of the talent show.
The 53-year-old was questioned about widespread reports he is expecting his first child with New York socialite Lauren Silverman.
Asked if his schedule would be affected by being a father, he joked: “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.”
Mrs Silverman also broke her silence to ask for “space and privacy” while “sorting things out” with her husband.
The 36-year-old who has a seven-year-old son, Adam, with her husband, said: “I am committed to sorting things out with Andrew as amicably as possible to ensure the well-being of our son. I would hope for some space and privacy in order to work through this.”
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 could be called to court after he was named as a “co-respondent” in Mrs Silverman’s divorce papers by her husband Andrew, according to a newspaper report.
Mr Silverman, a property magnate, had filed for divorce based on his wife’s adultery despite New York state allowing no-fault divorces.
Cowell’s mother is said to be “delighted” her son is to become a father for the first time.
Julie Cowell told a UK newspaper: “I’m delighted. It’s wonderful.”
According to the newspaper, the talent show judge fell for 36-year-old Mrs Silverman after her marriage hit the rocks.
Meanwhile, photographs emerged of Cowell and Mrs Silverman on a Caribbean holiday in January last year. Mr Silverman was also on the holiday and the trio are pictured on a yacht.
Britain’s Got Talent judge David Walliams tweeted about the news, saying: “Oh yeah, and @SimonCowell is doing a baby with a lady.” He added: “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!!”
One of Cowell’s other co-hosts offered her support. Former Destiny’s Child star Kelly Rowland, who has worked on the US and UK versions of X Factor, said she thought Cowell would be “a wonderful father”.
She said: “It’s not my news to share, but I do know about Simon and his character. He’s going to be a great dad.”