The All Blacks have been keen to commemorate the first 1905 meeting between the two countries and have planned a tour that includes all the home nations but were initially thwarted by Wales' reluctance to host an extra Test because of potential wrangles with clubs.
However, Wales have now suggested a November 5 date, with the All Blacks then going on to play already-scheduled Tests against Ireland, England and Scotland.
The New Zealand Rugby Union, though, are concerned that a match in early November will be too close to the National Provincial Championship final on October 22 and have suggested the match be played on December 3.
"We have been given this option [November 5] but our preference is a date at the end of the tour," NZRU chief executive Chris Moller said.
"The problem with that [November 5] is the time frame. It is only two weeks after the NPC final and we would like to have our top players in that competition.
"The end of the tour is much more attractive, but if that is not feasible for the Welsh then we have got to further deliberate if a two-week gap is enough for us before we play a possible Six Nations and Grand Slam champion.
"It would be a wonderful finale to the end of the year, especially if Wales win this weekend and are the Six Nations and Grand Slam champions."