The Coldplay frontman personally approached the 'Rude Boy' hitmaker to ask if he can submit some tracks for her next album because he is such a big fan of her.
He told Fresh 102.7 New York radio station: ''I don't even think she asked. I just said, 'Please can I try something?'''
Despite his impressive back catalogue, the singer/songwriter - who previously collaborated with Rihanna on the Coldplay track 'Princess of China' - is still worried his songs won't make the final cut.
He said: ''She has so many amazing people writing for her. It's like trying to win 'American Idol', getting a song on Rihanna's album.''
Chris - who split from his wife, Gwyneth Paltrow, earlier this year - confirmed him and Rihanna have been working in the studio together.
The 37-year-old musician - whose hits with Coldplay include 'The Scientist' and 'Fix You' - said: ''I love being in the studio with Rihanna. It wasn't necessarily with ... I was working for her.''
Chris also revealed he wants the 26-year-old pop superstar to appear on Coldplay's next album.
When asked if she would be making an appearance, Chris said: ''I hope so, yeah. I have a really nice song which ... maybe, I hope so.''
The actress thinks it would be tough to recast her character, Winifred Sanderson.
Beck wishes he'd had ''more fun'' when Kanye West invaded the stage in protest at his 2015 Grammy Awards win.
The Duffer Brothers wanted to "experiment a little bit".
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