The balls were from rugby ball manufacturer Leslie Rugby which had a clear out of stock with misprints on it, such as Otago Boys' High balls with the wrong crest.
A staff member at Leslie Rugby had tweeted about it to try to get the balls to Samoa.
Sports commentator Ken Laban was told and had asked Mr Little if he could arrange it.
Sports commentator and Wellington Regional Councillor had contacted Mr Little, who arranged to take them to dispense in Samoa instead, where they will be delivered to the village of Vaiala.
Mr Key will also have a meeting with Samoa's Prime Minister Tuilaepa Sailele Malielegaoi while in Samoa. Mr Key said it was the first All Blacks - Manu Samoa test match to be played on Samoan soil.
"Samoa and New Zealand enjoy a special relationship, including a shared love of rugby, and I am delighted to be attending this historic event."
He said the All Blacks had benefited from Samoan players and it was good that the NZ Rugby Union could give something back.
A number of MPs are travelling to Samoa for the game.
As well as Mr Key and Mr Little, other attendees include Sport and Recreation Minister Dr Jonathan Coleman, Immigration Minister Michael Woodhouse, Minister for Pacific Peoples Peseta Sam Lotu-Iiga, United Future leader Peter Dunne, NZ First Leader Winston Peters, and other MPs from National, Labour and the Greens.