The 72-year-old frontman said he had ended his bitter feud with fellow band member and younger brother Dave, and The Kinks are now planning to go on tour, reported Contactmusuic.
"Dave and I will definitely work together again. And we want to play live. Maybe The Kinks could play Glastonbury?"
Radiohead are the only band to be confirmed as one of the three headliners at the festival, due to take place in June next year.
Lady Gaga, The Stone Roses and Oasis are all rumoured to be performing, with betting reportedly suspended by bookmaker Ladbrokes on Ed Sheeran taking another of the headline slots.
The group enjoyed huge success in the 1960s and 1970s with
hits including "Waterloo Sunset", "You Really Got Me", "Sunny Afternoon", and "Lola".