A growing list of candidates have declared their interest in becoming the world's top diplomat, including UNESCO chief Irina Bokova of Bulgaria and former New Zealand prime minister and head of the UN Development Programme Helen Clark.
The Mandarin-speaking Rudd, who is based in New York as head of the policy institute Asia Society, served as Labor prime minister from 2007 to 2010 and again in 2013.
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"Kevin Rudd has requested that the Australian government nominate him and, as the prime minister has indicated on a number of occasions, that'll be a matter for cabinet," she told Sky News. "I'll certainly put the matter forward."
Candidates must be nominated by their governments, with Ban due to stand aside on January 1.
For decades, the choice of the UN chief has been in the hands of the Security Council and its five permanent members -- Britain, France, China, Russia and the United States -- in a process largely kept behind closed doors.
But the General Assembly last year voted to shake up the process, asking candidates to send a formal application letter, present their resumes and appear at hearings.
The final decision still rests with the Security Council, but the new openness could put some pressure on big powers to pick a nominee with broader appeal.
Rudd was elected Australian prime minister in the 2007 general election in a landslide defeat of John Howard, but in his first term was dumped by colleagues fed up with his style of management. He became foreign minister in Julia Gillard's government.
He remained popular with the electorate and Labor returned to his leadership in June 2013, making him prime minister for a second time.
However, he announced an end to his political career in November 2013, two months after losing elections won by conservative Tony Abbott.
A former diplomat who has long studied China, Rudd was an outward-looking prime minister whose love of travel earned him the nickname "Kevin 747".
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