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“As always, we love your enthusiasm and guesswork – but accurate news on headliners will be with you sometime in the new year!”
The report suggested a Glastonbury lineup with Dua Lipa headlining on Friday, Coldplay, who have headlined four times before, on Saturday.
Madonna would have then been the final act to close the festival on Sunday.
This arrangement would have marked the first time two female artists had occupied the premier headlining slots at the festival.
Last year, Glastonbury received criticism for having all-male headliners, featuring Arctic Monkeys, Guns N’ Roses, and Sir Elton John.
Explaining last year’s lack of female headliners, Eavis said: “I’ve always been really passionate about gender split [on festival line-ups] and I think, actually, our problem was that I’d been so outspoken about it that having a year when there wasn’t a female sent people a bit mad – or some people.
“And we did have a female – she pulled out and we replaced them with Guns N’ Roses. But everyone knows that it’s top of my list.
“It is difficult with female artists because there aren’t enough headliners. But we’re also creating them. We’re putting the bands and female artists on smaller stages and bringing them through all the time.”
Teasing the upcoming acts, Eavis said: “And who knows? Next year we might get two. And certainly, I can say that the legend is female.”