The track, which is rumoured to have been reworked by The Chemical Brothers, features Noel Gallagher on lead vocals.
It is not known if this is the finished version of the track or whether it will appear on their forthcoming Dig Out Your Soul LP.
'Falling Down' appeared on various file-sharing websites on Friday.
Oasis release Dig Out Your Soul on October 6. It is preceded by new single 'The Shock Of Lightning' on September 28.