The British band, who recently teamed up with Demi Lovato to record a track, planned to work with Gwen on a track but negotiations fell through after they had already recorded their part.
Grace, 32, who also plays cello in the group, revealed she was left crestfallen by the snub - as she idolises the No Doubt singer.
"(A song) was recorded but then it fell through, which was devastating," Grace huffed. "She was my childhood idol, so that was a real shame."
The group also wanted Bruno Mars and Harry Styles to appear on their forthcoming album "What Is Love?" but were turned down. They did manage to bag a collaboration with Elton John - only for them to decide his songs didn't fit with the rest of their new material.
"We realised there was a sound developing in a certain part of the Venn diagram of the album and we wanted to push that," explains bassist Jack Patterson. "It was kind of this tropical, plastic-y, mournful sound, whereas his songs were more from the (their 2014 hit) 'Rather Be world'."
Clean Bandit have become known for their star-studded collaborations - but almost split-up over who should sing on one of their biggest hits, "Rockabye" - a track which ended up featuring Anne-Marie and Sean Paul. The track originally featured its Norwegian co-writer Ina Wroldsen - but she was replaced at the request of record company executives against the band's wishes.
"I did feel like I couldn't do it any more because the idea that my business was hurting people," Grace explained. "That was really painful. I went completely crazy for a while after that. I just had to carry on, but inside it was really hard."