"For too long, the IMF's legitimacy has been undermined by a convention to appoint its senior management on the basis of their nationality," Australian Treasurer Wayne Swan and South African Finance Minister Pravin Gordhan said in a joint statement. "In order to maintain trust, credibility and legitimacy in the eyes of its stakeholders, there must be an open and transparent selection process which results in the most competent person being appointed as managing director, regardless of their nationality."
There is a range of possible contenders for the top job at the International Monetary Fund. Find out about some of them
Christine LagardeFrench finance minister-France
If the post goes to a European, French Finance Minister Christine Lagarde, 55, looks like the leading candidate. A flawless English speaker, she was voted best finance minister in Europe by the Financial Times in 2009. Counting against her is her nationality since so many previous IMF chiefs have been French.
Peer SteinbrueckFormer German finance minister
Mr Steinbrueck, 62, is a long-shot to become IMF chief, in part because he alienated allies of Germany with his fiery rhetoric while serving as finance minister in conservative Chancellor Angela Merkel's "grand coalition" from 2005 to 2009. He also alienated the United States by openly blaming it for the global financial crisis.
Axel WeberFormer head of Bundesbank
Mr Weber, 54, stunned Europe by announcing in February that he would be stepping down early from his post as head of the German central bank, the Bundesbank. Like Mr Steinbrueck, Mr Weber has a reputation as something of a loose cannon, who speaks his mind without regard to political or diplomatic constraints.
Kemal DervisFormer economy minister
Mr Dervis is credited with bringing Turkey back from the brink after a disastrous 2001 financial crisis, by pushing through tough reforms and helping secure a multi-billion dollar IMF bail-out. He had previously risen to vice-president at the World Bank. Seen as a leading candidate if the IMF post goes to someone outside central Europe.
Trevor ManuelEx Finance minister
Mr Manuel, 55, is well-respected in global financial circles, having served as finance minister of South Africa from 1996 to 2009. Born in Cape Town under apartheid, he was imprisoned repeatedly by the South African government for political activities in the late 1980s.
Agustin CarstensGovernor Bank of Mexico
Mr Carstens, 52, has spent most of his professional career as an economic policymaker in his home country, becoming governor of the Bank of Mexico in January of last year after previously serving as the bank's chief economist. He had a successful stint at the IMF from 2003 to 2006.
Gordon BrownFormer UK Prime Minister
The 60-year old former UK prime minister and finance minister has long been seen as a candidate for the IMF job or another big international financial post. But his successor David Cameron - whose support he would need - has dismissed him as a "deficit denier", adding that it was time to look beyond Europe.
Tharman ShanmugaratnamFinance minister/deputy prime minister
The 54-year-old has been the country's finance minister since 2007 and on Wednesday added the new job of deputy prime minister. With degrees from the London School of Economics and Harvard. He recently became the first Asian to hold the post of chairman of the IMF's policy advisory committee.
Montek Singh AhluwliaEconomic adviser to India's PM
Mr Ahluwalia, 67, is an influential economic adviser to Indian Prime Minister Manmohan Singh and has been a key figure in the country's economic reforms from the mid-1980s onwards. He supports open markets and has pushed the government to end fuel price controls and remove barriers to foreign business. His age may count against him.
The duo are co-chairs of the G20's (Group of 20 leading rich and developing countries) IMF Reform Working Group. Emerging economies have been calling for an end to Europe's traditional grip on the IMF leadership post.
Although support in Europe has been growing for Ms Lagarde, former South African finance minister Trevor Manuel also has been raised as a possibility.
Other contenders include former German finance minister Peer Steinbrueck; Axel Weber, the former head of the German central bank, the Bundesbank.
Mr Osborne said Ms Lagarde would be elected on a "merit-based candidacy, as she's been an outstanding finance minister and has chaired the G20 finance ministerial meetings this year in an effective and consensual way".
BBC Berlin Correspondent Steve Evans says Ms Lagarde has now also been endorsed "by the two people who matter in the German government".
Chancellor Merkel said Ms Lagarde was "distinguished" and "very experienced", and the finance minister, Wolfgang Scheuble, told the Bild on Sunday newspaper that she was "outstandingly qualified" and "extremely respected and appreciated in the entire financial world."
Mr Scheuble told the German newspaper: "The US and Europe pay by far the biggest share of the contributions.
"It's like in a publicly traded company: Those who hold the majority of shares will also get to name the chairman."
Meanwhile, Belgian Finance Minister Didier Reynders appeared to also express an interest in the top post.
Asked by a journalist on public television channel RTBF if he would be interested in the post, he replied: "But of course, these are the kind of jobs one could not refuse." However he also conceded that Ms Lagarde was Europe's favourite candidate.
Mr Strauss-Kahn was the fourth Frenchman to have held the IMF's top job.
He is in New York on bail awaiting trial for sexual assault and attempted rape, charges he denies.
In their statement Mr Swan and Mr Gordhan said G20 leaders wanted to reforming international financial institutions, including the IMF and the World Bank.Developed industrialised countries currently control about 57% of the voting rights in the IMF, compared with about 43% for developing nations.
With the recent emergence of Brazil, Russia, India and China, many other global figures - including the head of the Organisation for Economic Co-operation and Development - had also called for the IMF job to go to a non-European.