The actress, who plays Rosalie Hale in the vampire franchise, had previously been linked to co-star Robert Pattinson before rumours emerged that she was dating Latsis.
Speaking to E! News, a friend said: "They met about six months ago and have been together since. The reason she travelled over to Greece was to be with [Paris]. Both families have met, and really like each other. That's how serious it's getting between [them]."
The unnamed source added: "Robert Pattinson is nowhere on the radar. She's upgraded, in her mind."
Hilton ended her engagement to Latis in October 2005 amid reports that his father thought their relationship was not serious enough.
Reed, 21, recently wrapped production on Twilight sequel New Moon, which is scheduled for release in November.