Singer Neil Tennant told BBC 6 Music that the duo's only appearance at the festival in 2000 was so enjoyable that they want to return for the event's 40th anniversary next June.
Tennant said: "We played the main stage at 9.30pm on Saturday night, and it was an amazing experience as we wondered whether Glastonbury wanted to see the Pet Shop Boys - whether we were too dance or pop or something for them, but it really went down fantastically well."
The frontman went on to say that if festival boss Michael Eavis did invite them, they would look to enlist several special guests for their performance.
He added: "A good song for us to do with people is 'What Have I Done to Deserve This' as sadly Dusty Springfield isn't around anymore. We've done it with Melissa Etheridge in America before, Lady GaGa at the Brits, Cerys Matthews from Catatonia when we did Glastonbury 2000... there's always a little vacancy there for someone."
Earlier this month, Pet Shop Boys revealed plans to release a Christmas EP, scheduled for December 14.