"Unfortunately at this moment I have to keep it private," the 53-year-old "X Factor" judge said.
"There are a lot of things I will eventually clear up when the time is right, but I really have to be sensitive because there's a lot of people's feelings involved here," he later told People.
He's referring, of course, to the feelings of Lauren Silverman, the 36-year-old New York socialite pregnant with his child, and her husband, real estate mogul Andrew Silverman.
Andrew filed for divorce on July 23, citing adultery as the reason behind the split and personally naming Cowell as the third party.
"My top priority is protecting my 7-year-old son while working to resolve all outstanding issues with my wife," he said in a statement Thursday. "Hopefully people can respect the interest of our child during this process."