Both associations agree that a Saturday afternoon kickoff on November 11 in Wellington is ideal, given the challenges of getting their players from Europe, North America and South America to New Zealand in good time.
A Saturday afternoon match is also commercially much more valuable, believed to be worth twice as much in broadcasting revenue than a Friday night match, due to the time zones of the South American market.
But playing the first leg on Saturday afternoon would make it difficult to complete the tie within the confines of the Fifa window.
Both teams wouldn't be able to depart for South America until Sunday morning (NZT), and even though they would gain almost a day on their travels, the earliest they would arrive in Lima would be Sunday night (local time).
That would leave only one full day (Monday) to prepare for the match, which would kick off around 9pm on the Tuesday (Peru time) in Lima.
NZF are prepared to operate within those tight boundaries if necessary.
But NZF would prefer more time, while the Peruvian football association are unlikely to consider such a venture, given South American windows usually operate with at least four clear days between fixtures, as well as much reduced travelling time.
That's why the push for the second leg to be played on Wednesday, November 15 (Thursday, NZT) has emerged. It would mean that the respective sets of player would arrive back at their clubs in Europe and the United States a day later, but from a New Zealand perspective, the timing wouldn't be much different from the recent window in September, when the players had to make the convoluted journey from the Solomon Islands on the Wednesday morning after a Tuesday afternoon match in Honiara.
It's not yet known if Fifa will allow such a request. However, there is a precedent. In 2013, Fifa brought forward the front of the window by two days for New Zealand and Mexico, given the logistical demands at that time. However, that agreement was put in place several months before the respective matches, and Fifa may be reluctant to act on relatively short notice this time.
But ultimately it comes down to an issue of player welfare, and Fifa will also want to be seen as taking the lead in such an important area.