Jennifer and Owen are said to have become inseparable while filming Marley and Me and are openly flirting with each other on the Miami set.
One crew member told America's Star magazine: "The hugging didn't end when the cameras stopped rolling. They were very flirty together, far more than you would expect. In between takes they were hanging onto each other. They are very friendly."
Although the former Friends star was said to be worried about working with the comic star, she has been surprised by the chemistry between them. A friend of Jennifer's added: "She wasn't looking forward to the film at first because she was worried about working with Owen, but he has turned out to be a real surprise. She's finding out that he's a terrific guy who's fun to be around.
"Jennifer is known for being a recluse on set. But she's having so much fun hanging out with Owen. She's just really relaxed and happy, which is nice to see."
Last week, it was claimed the 39-year-old actress was dating Brian Bouma, a crew member she met while filming Traveling in Vancouver, Canada. Owen was rumoured to have rekindled his romance with Kate Hudson, after they were seen together in Malibu last month.
Jennifer, who is reportedly desperate to settle down and become a mother, is now struggling to decide whether to choose Owen or Brian.
A pal of the star told America's OK! magazine: "Both men have some of Jennifer's favourite qualities. Brian has the height and looks, while Owen can make her laugh. Either one would be a good choice for Jennifer.
"Owen isn't seeing anyone seriously - he wants to keep his options open. As far as Brian goes, Jennifer is keeping her options open about him! Brian's a really good guy. He's a bit overwhelmed by all the attention since he's been identified as Jennifer's boyfriend. They still talk on the phone with each other."