Britain is the one permanent member of the council supporting change.
The discussion on the selection was prompted by a grouping of 27 countries in the United Nations known as ACT - the Accountability, Coherence and Transparency group, including New Zealand.
ACT wrote to the president of the Security Council last month when Malaysia was in the chair for the month.
It did nothing with it so New Zealand put it on the agenda - although New Zealand is not leading the pack lest it be seen as trying to gain some advantage for former Prime Minister Helen Clark, a potential contender, and currently head of the UN Development Programme.
The ACT letter described the present system as "a concealed process with exclusive participation."
Its proposals include getting the presidents of the UN General assembly and the Security Council to jointly invite all member states to nominate candidates, to have a closing date and set out a timetable for following steps.
ACT is one of several groups campaigning for reforms.
Other groups are campaigning for the next appointment to be a woman.
Mary Robinson, a member of the UN "Elders" group has suggested a seven year non renewable term instead of the current five-year term, renewable for another five.
The argument goes that the possibility of being renewed makes Secretary Generals too weak in their first terms and less likely to stand up to the permanent five on the Security Council who can veto their second term, or first.
More discussions are set down for both the Security Council and General Assembly.
Foreign Minister Murray McCully said yesterday that the selection of the next Secretary General was a 2016 issue, not one for 2015.
"The Prime Minister has always been very clear that if Helen Clark was a contender, she would enjoy the full support of the New Zealand Government but she and we both understand that there is a process that plays out.
"There is a rotational system. It is regarded as Eastern Europe's turn to put forward a candidate but we know from previous occasions that the politics within Eastern Europe are pretty challenging."
He said the sensible thing to do would be to show some respect for the processes that are in operation.