The music festival's founder Michael Eavis has revealed that he is interested in booking the iconic band to headline the Pyramid Stage in 2013.
"On a good day, if the weather's fine, [Glastonbury] is an interesting proposition," Richards told BBC 6 Music.
"The band wants to get these four gigs under their belt and then think about next year after that."
The Rolling Stones will play two shows at London's O2 Arena in November and a further two at Newark's Prudential Center in New Jersey in December.
Asked if they would continue touring next year, Richards added: "Anything is possible. This band isn't going to wind up with four shows."
The band will celebrate their 50th anniversary with a greatest hits collection GRRR!, released in the UK on November 12 and a day later in the US.
Listen to the Rolling Stones' new track 'Doom and Gloom' below: