On Friday morning the Security Council will hold the first 'straw poll' to narrow down the field of 12 candidates so far but others can still join after that point. The Security Council is expected to pick a final candidate by October.
So far there are 12 candidates for the role, not including Rudd. They are Irina Bokova (Bulgaria), Helen Clark (New Zealand), Christiana Figueres (Costa Rica), Natalia Gherman (Moldova), Antonio Guterres (Portugal), Vuk Jeremic (Serbia), Srgan Kerim (Macedonia), Miroslav Lajcak (Slovakia), Igor Luksic (Montenegro), Susana Malcorra (Argentina), Vesna Pusic from Croatia, and Danilo Turk (Slovenia).
It is considered to be Eastern Europe's turn to hold the post although Clark has argued it should be based on merit rather than region.
Clark's argument that the role should be selected on merit rather than region was echoed last week by the The Elders - a group of global leaders established in 2007.
Elders Mary Robinson, former President of Ireland and UN High Commissioner for Human Rights, and Lakhdar Brahimi, former Algerian Foreign Minister and UN diplomat, said the key decision would be made by the Security Council.
"It is crucial that that the five Permanent Members collectively recognise that merit must trump all other considerations, including regional rotation and gender ... Only an independent and courageous Secretary General, someone capable of building consensus and, at the same time, showing real moral leadership, can give the UN the confidence and credibility to gain lasting peace in our time."
They also called for a change to one seven year term rather than a five-year term with the option of a second term. They argued would allow a Secretary General to make changes such as reform of the Security Council without fear of jeopardising re-election hopes.