Radiohead frontman Thom Yorke has suggested the band could be set to work with Jack White, according to reports.

Radiohead were headlining the Bonnaroo Music and Arts Festival in Manchester, Tennessee, when Yorke indicated that the band could be about to collaborate on a project with the former White Stripes guitarist and singer.

During the performance on Friday night, Yorke dedicated the new Radiohead song Supercollider to White, before making a cryptic announcement to fans, according to Billboard magazine.

"This song is for Jack White. We saw him yesterday. A big thank you to him, but we can't tell you why. You'll find out,” Yorke is reported to have said.

White’s record label, Third Man Records, is based in Nashville, Tennessee, a little over an hour away from where the annual four day music festival is held.

The magazine speculated that the meeting may have been to discuss the prospect of Radiohead making a single with White, or Yorke working on a separate project with the Blunderbuss singer.

White recently worked with Beck on one-off single I Just Started Hating Some People Today while the American singer-songwriter was in the Tennessee area, sparking rumours that Radiohead could be working on a similar collaboration.

Outside of the band, Thom Yorke has worked with a number of other artists, including PJ Harvey, Björk, DJ Shadow and the various members of his group Atoms for Peace: Flea of the Red Hot Chili Peppers, and Beck.

Radiohead are currently on a world tour to promote their album The King of Limbs, and have debuted a number of new tracks for US audiences.

The band will be back in the UK in the autumn to play their first British dates in more than three years. The tour will kick off with a concert at the Manchester Evening News Arena on October 6, and two shows at London's O2 Arena on October 8 and 9, before they undertake a full European tour.