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Fleming's band has been nominated for their second album Two Dancers, while Bailey Rae has also received a nod for her second record, this year's The Sea.
Asked who he would like to win the award, Fleming told DS: "There's a few. We've got some genuine friends on there. We'd love to see Villagers win it.
"Foals toured with us for a long time who were unfairly overlooked with their first album so I think that'd be wonderful for them."
He quipped: "We always said of The xx that if we were nominated we'd only be there to see them pick it up!
"But my tip for it has to be Corinne Bailey Rae. If I had to put money on it that's who I'd put money on. I dunno why, I just have a feeling!"
Of this year's shortlist, Fleming added: "A criticism I always had about the Mercury Prize was that it didn't necessarily represent the best albums of the year - but it's such a high-profile thing, there has to be an engagement with the mainstream to make it even remotely interesting to most people.
"Some albums, like Kit Downes Trio or Villagers, to put those in the same company as Paul Weller and Laura Marling and Mumford & Sons is definitely going to improve their profile, whereas if they were in with King Midas Sound maybe it wouldn't."
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