But don't ask Simon to call it anything more than dating.
"Girlfriend?" he said, when pressed about the couple's budding relationship. "We're people who date. She's adorable, isn't she?"
The pair have been spotted together several times since September. Just last month, Electra hinted to "Access Hollywood" about her growing friendship with the media boss.
"We worked together on 'Britain's Got Talent' ... I really like him. I think he's really cool. Now, obviously he's in town (Los Angeles) with the 'X Factor' and we've started to hang out and we've become friends. I think he's a great guy."
Cowell split from his make-up artist fiancee Mezhgan Hussainy earlier this year. Electra has been married twice. Where do you think their love will lead them?
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