Jeremy Corbyn has been asked to address more than 130,000 music fans from the main stage on the final day of the hugely popular event, sources told the Press Association.
John McDonnell has been invited to speak at the festival’s Left Field, where pop and politics mix.
The line-up of speakers and groups at the Left Field is being organised by singer and activist Billy Bragg.
Union leaders have taken part in debates at Glastonbury in previous years but Mr Corbyn would be the first party leader to appear.
Most people attending the festival will be in Glastonbury on June 23, the day of the European Union referendum.
A Labour Party source confirmed Mr Corbyn had been invited.
Adele and Muse are among the headline acts at the festival, which takes place from June 22 to 26.