The pair first met at Relativity Media’s glittering Golden Globes bash back in January, and were spotted laughing with friends.
But after Olivia split with her Italian Prince hubby Tao Ruspoli it seems things have become a little more than friendly between the pair.
The Tron star has reportedly paid several sneaky visits to Ryan in Ohio, where he’s filming flick The Ides of March with A-lister George Clooney.
And earlier this week, the new couple were spied on a secret date at the Cincinnati aquarium trying to stay incognito as they strolled around hand in hand.
Ryan and Olivia were even snapped by am eagle-eyed fan, who filmed them as they walked around the attraction, but the pair have yet to comment on the relationship.
Do you think Ryan and Olivia would make a cute couple? Let us know your thoughts in the comments box below.