Jason Fisher, the Tolkien scholar, quotes note 3 from Letter #259 (Letters) at his blog Lingwë:
'A long unpublished poem entitled 'Volsungakviða En Nyja', probably written in the late 1920s or early 1930s. Tolkien described it, in a letter to Auden dated 29 January 1968, as 'written in fornyrðislag 8-line stanzas in English: an attempt to organize the Edda material dealing with Sigurd and Gunnar',
which is probably the first lead to the contents of this new book.
According to the Companion & Guide by Wayne Hammong & Christina Scull (Reader's Guide, p. 654), the poem, called ‘Völsungakviða En Nýja' ('The New Lay of the Völsungs'), consists of 339 eight-line stanzas. There is also written there exists a companion poem from the same period, called Guðrúnarkviða en nýja ('The New Lay of Gudrun') of 166 eight-line stanzas. If this is the case we can speculate that both will be published together in this new book.
In 'Digging Potatoes, Growing Trees: A Selection from 25 Years of Speeches at the Tolkien Society's Annual Dinners: v. 2 (Peter Roe Booklets)',we can read Rayner Unwin saying
'[...] in fact, when Christopher can have his sabbatical and get on with some of the other things that he needs to do - that I want him to do, rather - like the book of his father's long, non-Middle-earth poems, 'The Fall of Arthur' and the new 'Volsungasaga' and a few other things. These exist and need to be brushed up and put into a volume but, understandably enough, Christopher doen't want to get distracted from the stream of conciousness which HoMe obviously demands of him'.
Maybe this is the 'new Volsungasage' Rayner Uwnin talked about, and who knows that some of the other works might also someday see publication!?
Jason Fisher also speculates that the book might be very short, since Tom Shippey has written that there is an 8-page gap in the Codex Regius manuscript of the Poetic Edda, specifically in the Sigurðr cycle [Roots and Branches: Selected Papers on Tolkien, p. 192]; and if Tolkien’s poem was meant to fill that gap, as Shippey supposes, then there is indeed a reason to think it must be fairly short. Let us hope that it is not!