He firmly denied the accusation. Addressing the identity of the woman, he said, "It is someone that I know who is an acquaintance that I thought was a friend."
Atlanta-based station Fox 5 is expected to run a report on the charges early Monday evening. Cain said he wanted to act preemptively before the claims came to light.
"I wanted to get out in front of it," he said. "I have nothing to hide, I have done nothing wrong."
The presidential contender suggested that "an infinite number of people" could come forward with similar allegations against him.
Cain signaled that he has no intention of abandoning his campaign for the White House. He said as long as his wife is behind him, he's in it to win it.
UPDATE: The new accuser, an Atlanta businesswoman named Ginger White, sat down with FOX News to tell her side of the story.
“It wasn't complicated," she said. "I was aware that he was married. And I was also aware I was involved in a very inappropriate situation, relationship.”