The British singer ''froze'' after the superstar introduced herself on a long-haul flight and has been kicking himself ever since for not uttering a single word when she congratulated him on his newfound success across the Atlantic.
He exclusively told BANG Showbiz: ''I was on a plane back to the UK from LA and someone tapped on my chair and it was Rihanna. I was so shocked. And she just said, 'Congratulations on everything' and walked off.
''I literally didn't say anything I was so shocked and I was like, 'Why didn't I say anything?!' I just froze, but it was crazy. Of course when I tell that story to my friends it's much cooler, I say we hung out, she came back to my place, we chilled for a bit. Not that I completely froze!''
The 'Can't Say No' hitmaker confessed he was less starstruck when he got in the studio with producer Pharell Williams because the meeting was set up in advance and he'd had months to plan his nonchalant greeting and to control his nerves.
Conor, 20, explained: ''I get the most starstruck when I don't expect it. I was recording with Pharrell Williams and I thought I'd be cool because I knew about it months in advance, I knew I was going to meet him and be in the studio with him.
''Months of preparation in my head in order to not scream when I saw him, but it was tough!''
Conor is one of three stars, along with Rita Ora and Delilah, who have teamed with MasterCard to search for a fan to star as them in a remake of one of their music videos.
The lucky winners' clips will feature in the BRIT Awards 2013 TV advertising breaks. The successful fans will enjoy wardrobe, hair, make-up and professional dancers, and will work on their videos with award-winning director Emil Nava, as well as meeting their idols when they attend the BRIT Awards on 20 February. Visit somethingforthefans.co.uk for more information.