The price for Gallaher's shirt is expected to top the world record for a rugby jersey, set in May when a fan bid 21,500 for a New Zealand shirt worn during the same Originals tour.
Ben Rogers, from auctioneers Rogers Jones & Co, said: "The jersey is undoubtedly the most significant sport-related lot we have ever offered.
Wales versus The Originals, in Cardiff, is regarded as one of sport's greatest matches with over 47,000 spectators at the Arms Park. Even before kick-off the match had become a landmark game when the Welsh supporters sang the national anthem in response to the New Zealand player's stirring performance of the haka.
Gallaher was born in Ireland in 1878 and emigrated to New Zealand with his family in the 1890s.
He captained New Zealand's first official tour outside Australasia in 1905, in which they played in Britain, France and Canada.
They lost only one match, going down 3-0 in that same Welsh test in which the jersey was worn.
Gallaher played 33 times for his country and won six test caps, with his career briefly interrupted in 1901 when he served in the Boer War.
Ten years after his retirement from rugby he volunteered for World War I at the age of 42.
Gallaher was mortally wounded during the battle of Gravenstafel Spur on October 4, 1917, when a piece of shrapnel penetrated his helmet.
He was honoured in 2011 when a bronze statue of him was unveiled outside Eden Park.
The shirt for sale has the embroidered New Zealand silver fern badge and stitched canvas overlay to shoulders, upper chest and back area.
It is complete with leather v-shape neckline.
The auction is on October 9.
