The iconic UK band have never headlined the festival, despite being one of the biggest music acts of all time.
They have continued to be a huge live act following the death of Freddie Mercury, with Adam Lambert performing as frontman in recent years.
But Eavis has said they won’t be taking to the Pyramid Stage any time soon – and it’s partly because of a feud he had with Brian May.
In a new interview, he claimed that the band’s agent sent them a handwritten card in the hopes of landing a slot.
“It almost worked, I tell you,” he told the BBC – but added that the group are “not quite our thing.”
He added: “We had a whole row with [Queen guitarist] Brian May about the badgers – do you remember all that?”
Eavis and May fell out over badger culling – with Eavis in favour and May against. The former called the latter “a danger to farming”.
Asked if the row is why Queen haven’t played Glastonbury, he said: “Not really but it does have a bearing on it.
“I have to say, it does have a bearing on it.”
Glastonbury this year is being headlined by Stormzy, The Cure and The Killers.
Tame Impala, Vampire Weekend, Liam Gallagher, Janelle Monae, Bastille and current album chart topper Billie Eilish are also on the bill.
Queen have plenty of wind in their sales right now as it is, thanks to the overwhelming success of Bohemian Rhapsody.