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But the two, in fact, shared one special night together several years ago.
Cowell revealed on "The Howard Stern Show" yesterday that the two were once set up on a "bizarre kind of blind date" at the Polo Lounge in Beverly Hills.
"She turned up 8 months pregnant and had a dog in her handbag," Cowell said.
While Stern speculated that her pregnancy must have been a "turnoff," Cowell said he found her quite charming.
"[It was] a little bit [of a turn-off]," he said. "She is gorgeous. I liked her a lot, I think she's cute, funny, a bit of a wacko...but I like that."
He then mysteriously added, "We met up afterwards," providing us with a visual we hope we can quickly get out of our heads.