The body has always been headed by a European, and UK chancellor George Osborne has backed Christine Lagarde, French economy minister, for the post.
The position is vacant after Dominique Strauss-Kahn resigned last week so he could fight sexual assault charges.
"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
BACK 1 of 10 NEXT
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.
'Distinguished' 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.
Voting rights 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.