The 42-year-old actress reportedly enjoyed a romantic dinner date with the star at the Sunset Towers Tower Bar in West Hollywood last night.
A source told X17online: "Jen and Justin have recently started dating. They've known each other for a while, but they're more than friends now. They're cautious - they're both taking it slowly."
The pair allegedly arrived at the restaurant separately but left via an underground car park, ducking down in the back of a chauffeur-driven car which drove them to Aniston's Beverly Hills mansion.
The former Friends star, whose dog Norman died recently, was told by her Crete-born father that he would be happy if she settled down with a Greek man.
Watch the trailer for new Jennifer Aniston movie Horrible Bosses below: