According to The Sun newspaper, 'Jennifer and Darren have tried to keep things low-key and under wraps but they are really into each other.
'Recently Jennifer was working on a gruelling project and she relied on Darren for support and they were in constant contact. It seemed to show they were the real deal.'
The film also stars Javier Bardem, Michelle Pfeiffer, and Domhnall Gleeson.
Jennifer was most recently linked to Coldplay frontman Chris Martin, who she dated for four months last year.
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