The singer was approached to do a verse on the track, but failed to get back to the song's producer Jeff Bhasker.
"[fun.] said, 'Who can we get?' And I said, 'Let's get Rihanna'," Bhasker told MTV. "We were shooting for the stars on everything and she was kind of a muse."
He added: "Someone tried to reach out and I know she heard the song and liked it. But I think some wires just got crossed."
Janelle Monáe featured on 'We Are Young' in the end, with the song going on to become one of the biggest hits of 2012.
What's more, the beat on the track was nearly turned into a Jay-Z and Kanye West track for their Watch the Throne album.
"They were going to rap over the beat," Bhasker said, "but everything gets changed at the last minute."
Watch the music video for fun.'s 'We Are Young' below: