The 'Set Fire to The Rain' singer has said she is too afraid of performing in front of thousands of people to headline the festival - which returns next year - but organiser Emily is hopeful she can recruit her to help balance between the number of male and female performers at the event.
She told Spotify's official blog: ''Well, she played on the Park Stage at 10 in the morning a few years ago, so that's not going to happen again! That was a really rainy year, but hopefully that's not what put her off festivals.
''I think she'll do what she wants to do, let's face it! It would be great if she played, but obviously, but she'll make that decision. There aren't that many girls to be honest, so that's another job of ours, to keep the balance right.
''It would be brilliant to see her go all the way to the Pyramid Stage. But who knows? She doesn't like playing to large crowds, but if you can perform at the Grammys, she could do it.''
Other acts on Emily's wish list include Prince and The Rolling Stones although she concedes they would have to lower their fees to appear.
She said: ''The obvious ones are Prince and The Stones, both of which would obviously be great. There was a lot of talk of Prince last year, but I don't know if that will ever happen, to be honest. The same with the Stones, but it's hard for us to accommodate people that are used to doing their own thing, but, you know, that was OK for Bruce Springsteen and Sir Paul McCartney.
''We can make anything work, we just need the band to be up for it. And obviously we just pay a lot less, but we offer other things.''