The birds - two kiwi, two tui, two fantails, a red-crested parakeet and a long-tailed cuckoo - were stuffed and presented in a large glass case.
The case bears the mark of the item's maker, William Smyth, of Stanley Cottage, Main South Rd, Caversham.
The work is dated January 1879.
Hayward's Auction House owner, Kevin Hayward, said he had high hopes for the piece, which was "exceptionally" rare, given how many birds there were in it, its excellent overall condition, and that it still had its provenance attached.
At a recent auction in Australia a single kiwi in a glass box sold at auction for up to $5280.
He hoped to fetch anywhere from $5000 to $10,000 for the display.
The item was a part of the estate of Dunedin natural history photographer George R.
Chance, from which there were several items in tomorrow's antique and collectable auction, including a camera belonging to the photographer.
The Leica camera was imported from Germany in 1954 by Mr Chance and comes with accessories and provenance, including the original receipts.
