The band were allegedly asked by organisers to feature in a Symphony of British Music segment of the celebrations, which aims to showcase a history of UK talent.
The group decided against appearing at the ceremony over a financial disagreement, reports The Times. Acts are being offered a nominal fee of £1 for their participation.
However, a source told the newspaper that they still have a great lineup planned for the Symphony and are keen to have the remaining members of The Clash perform 'London Calling'.
Sir Paul McCartney, the Spice Girls, Adele, Sir Elton John, The Rolling Stones and Take That have all been rumoured to make up A Symphony of British Music.
> Sex Pistols sign new record deal ahead of album re-issue
Watch the Sex Pistols perform 'Anarchy In The UK' live in 1976 below: