Frontman Thom Yorke indicated that the band could be one of the three acts to top the bill on the Pyramid Stage this summer.
While the singer dismissed rumours that his side-project Atoms For Peace would play the festival, he told BBC Radio 1's Zane Lowe that "parts" of the group would appear in some way.
The hint immediately caused speculation that Radiohead would play the music event, and placed them with The Rolling Stones, Fleetwood Mac and Mumford & Sons as rumoured headliners.
Glastonbury festival will return on June 27-30 after a scheduled year off in 2012 to let the site at Worthy Farm recover.
U2, Coldplay and Beyoncé topped the bill back in 2011.
Watch the music video for Radiohead's 'Lotus Flower' below: