The man has been accused of the murder of British backpacker Grace Millane and in December Google emailed his name to anyone who signed up to its "what's trending in New Zealand" email, the New Zealand Herald reported.
Little had sought an explanation from Google executives whom he met at the country's parliament in December and company officials had told Prime Minister Jacinda Ardern during a January meeting in Europe that they would examine the matter.
Similar assurances were given to officials of Little's ministry when they followed up with Google in March and also this week.
He said he did not accept the claim that it was a rare case and that Google was not a published.
Little told the ABC's PM program that Google had sent the information to New Zealanders on its own initiative and it was residing on the company's servers.
He said it was not a case of people in New Zealand seeking out the information and then locating it.
Little said he did not accept that Google was not a publisher as it actively sought out information through its own algorithms and then generated that information when people looked for it.
He was not clear as to what he could do but said that some solution had been found as there was a risk that this kind of leaking of suppressed information could surface on the search platform again.