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Gallagher has in the past mocked Wilson's group for wearing make-up and described them as "just a bad Blur". Wilson responded by claiming that "Oasis have disappeared up their own arse".
Asked if he had heard Gallagher's post-Oasis output, Wilson told Digital Spy: "Yeah, I've got the record - I got it on the day it came out. I like it! It is what it is, it's brilliant.
"[Kaiser Chiefs songwriter and drummer] Nick [Hodgson]'s been to see them I think three times - I haven't seen them yet. But yeah, good on him."
He added: "He's done what he said he'd do. I doubt he cares what anyone thinks, but yeah. I like Beady Eye."
Of reports that the Kaiser Chiefs had turned down a lyric from David Bowie, Wilson said: "Nick said something and [producer] Tony [Visconti] said something and you know that in between every opposing tabloid story the truth is somewhere in the middle - and a lot more boring.
"A story's a story. I don't really know about that. I'm not going to talk about it!"
> Kaiser Chiefs' Ricky Wilson shakes up the music business: Interview
Watch Kaiser Chiefs cover The Small Faces' 'Lazy Sunday' below:
