Glastonbury could be on the move to a new site
Farm owner Eavis, who runs the event with his daughter Emily, told the BBC that he has located another site "100 miles up towards the Midlands" that might be used in 2019.
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Hide AdHe said he is considering the move to help protect the main site.
However, Eavis indicated that he would be reluctant to see the festival move from its home permanently.
The 81-year-old said: "I am arranging for one year off, say every fifth year or so, to try and move the show to a site that's more suitable, I have to say.
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Hide Ad"But it would be a huge loss for Somerset if it went there forever, would it not?
"But I've found a site about 100 miles up towards the Midlands."
Eavis said he felt the festival - which attracts more than 170,000 music fans - would work anywhere, but added: "I don't want to lose it forever, no way."
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Hide AdNext year the festival will be held at its usual location at Worthy Farm in Pilton, Somerset, with Radiohead the first band confirmed to headline.
The event is taking a year off in 2018.
Earlier this year it was reported that Eavis was in talks with the Longleat Estate in Wiltshire about holding the festival there, amid concerns about future agreements with landowners at the present site.