The tracks, recorded over a decade ago, were due out on Friday to mark the one-year anniversary of the star’s death.
The new album, titled Deliverance, was announced by music engineer George Ian Boxill, a Grammy and Golden Globe award-winning sound mixer responsible for many of Prince’s albums.
But according to court documents filed by Prince’s estate and Paisley Park Enterprises, Mr Boxill has no right to release the songs.
They claim he is trying to exploit the music for personal gain and demand all of the tracks are returned.
The lawsuit reportedly claims there was a 2004 confidentiality agreement, where Mr Boxill agreed all the recordings would remain Prince’s exclusive property.
Prince sings, and plays guitar and keyboards on the songs.
It is unlikely to be the only batch of unheard tracks to be fought over in the coming years.
After he died from an accidental drug overdose in April last year, the legendary vault was opened at his Paisley Park studios containing his archive of concert recordings, unreleased songs and rehearsal tapes.
Last year, unreleased track Moonbeam Levels appeared on the compilation Prince 4Ever.
An expanded version of Purple Rain is also due out in June, containing two albums and two unheard concert recordings.
Prince’s estate has also signed a $30m (£23m) deal with Universal Music to release non-Warner Bros material.
His 1980s band, The Revolution, is also back together and will kick off a three-month tour by performing at Paisley Park this week to mark a year since his death.