The 81-year-old American crooner was being interviewed at Cheltenham Literature Festival when he spilled the beans.
“I had asked him if he had any plans to play any more gigs and he said he had been asked to play at the festival,” explained BBC Radio 4’s “Front Row” show host John Wilson.
Glastonbury sold out its 137,500 capacity in 12 hours when tickets went on sale at the beginning of October.
The only act announced was The John Vistic Experience, which earned its slot by winning the festival’s rock competition.
Speculating on who will play Glastonbury has become an annual pastime in the U.K., while Eavis and his team do as much as possible to keep the lineup secret until the festival’s ready to announce it.
William Hill bookmakers reckons The Rolling Stones are a favourite to headline, quoting the act at 4/1, with Coldplay and David Bowie at 8/1, Muse at 10/1, U2 and Arctic Monkeys at 12/1, and Radiohead at 14-1. There was no price on offer for Williams.
Click here for the complete BBC report.