By Ben Leach
The improvised recording was made in 1967 and was played just once in public. But it was never released because three of the Fab Four thought it was too adventurous.
It is said to be composed of a series of shrieks and psychedelic sounds - far away from the melodious recordings with which the Beatles are associated.
But speaking on a BBC Radio 4 arts programme to be broadcast this week McCartney said that the public would get a chance to listen to the track.
"It does exist," McCartney told John Wilson, the presenter of Front Row.
He added that he still has a master tape of the recording and suspects that "the time has come for it to get its moment".
"I like it because it's the Beatles free, going off piste," he added.
The track was put together on 5 January 1967, in between working on the vocals for the song Penny Lane.
Since it was recorded 40 years ago the track has achieved almost mythical status for Beatles fans.
It is reported to include the sounds of gargled water and strangled shouts from John Lennon which clash with church organs and distorted guitar.
"It will help reaffirm McCartney's claim to have been the most musically adventurous of all the Beatles," said Mr Wilson.
"He told me he would love to release the track. All he needs now is the blessing of Ringo Starr, Yoko Ono and George Harrison's widow Olivia."