The pair have reportedly become close since shooting romantic comedy 'Playing the Field' together, and they were seen at the end of last week riding along the Pacific Coast Highway in California.
Jessica and Gerard were wearing leather jackets and boots paired with sunglasses, and the actress tightly held onto the actor's waist as they drove around the Topanga Canyon.
This is not the first time the pair have been seen out together. The two stars were recently spotted enjoying a cosy dinner at a Japanese restaurant in Louisiana, during which they sat side-by-side.
Jessica, 29, and Gerard have a history of being romantically linked to their co-stars.
The 41-year-old actor was rumoured to have dated Jennifer Aniston when they starred alongside one another in 'The Bounty Hunter', while the 29-year-old actress - who split from Justin Timberlake earlier this year - was previously linked to Edward Norton after they starred in 'The Illusionist'.