The US group's biggest hit - for which they won Song of the Year at the Grammy Awards last Sunday (10.02.13) - features Janelle Monae, but they admit they initially thought Rihanna's vocals would work better on the track.
Producer Jeff Bhasker told MTV: ''They said, 'Who can we get? And I said, 'let's get Rihanna.'
''We were shooting for the stars on everything and she was kind of a muse.
''But everything works out for a reason and Janelle Monáe worked out to be the perfect choice.
''She brought the right element of a great soulful flavour that we wanted for the album.''
Although Fun. were an almost unknown act at that time, they were dreaming of pop stardom and reportedly had pictures of Rihanna on their studio wall.
Jeff said the 'Diamonds' singer had heard the track, but never got around to recording vocals for it.
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.''
Guitarist Jack Antonoff has said the song best encapsulates the sound they were aiming for with their second album 'Some Nights'.
He said: ''It's pretty rare, because any other projects that we've done, I don't think any of us have ever had that song that was like, 'This is our band.'
''We're proud to say, 'Listen to this one song, and then come listen to the rest. Here it is.' ''