Here's some of what the Enquirer's source said, via Dlisted:
O.J. told me Khloe's his child. It was the big secret that no one in the two families would discuss. And Robert admitted he and Kris were not having sex at the time Khloe was conceived. O.J. bragged about his sex life and many female conquests, which he said included some of his best friends' wives.
He used to tell us way back - even before he and Nicole got divorced - that he had a love child with the wife of a wealthy family. But at the time of Khloe's birth, it would have been devastating for the news to come out that America's biggest sports hero had fathered a love child.