But the couple - who are both intensely private - are desperately trying to keep their relationship away from the media spotlight.
A close source says, "Renee and Damien have been seeing each other for a while and they're both really happy.
"Renee is pretty intense and Damien is something of a poet so they're the perfect match.
"They have been seen drinking in an Irish pub together and they certainly looked very cosy but it's early days."
The 35-year-old actress has also been spotted house-hunting in Galway, Ireland, fuelling speculation she now wants a home nearer the CANNONBALL hitmaker.20/02/2005 10:47