The celebrity couple are regularly spotted out together in Los Angeles, but have tried to keep their budding relationship under wraps.
A source confirmed the romance to Us Weekly magazine, adding, "They stay out of the limelight, but they spend a lot of time hanging out and working out together at Gold's Gym (in Venice Beach, California).
"They kiss and hold hands when they come and go from the gym. You can tell they're a couple."
The pair were romantically involved in a flashback sequence on Lost before they were both killed off.
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