The politics of choosing a new IMF leader have become part of the calculation in Europe, with those backing Mr Juncker arguing that Europe cannot afford to lose the managing directorship of the IMF by appointing Ms Lagarde to the commission post.
Senior emerging market officials say they will push hard for their candidates in the event of any IMF succession battle.
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"We would need to have a truly open process, with no geographic pre-determinism," said Paulo Nogueira Batista, the IMF executive director for Brazil and 10 other countries, although he stressed that the managing directorship was "not under discussion", despite the rumours surrounding Ms Lagarde.
But European determination, combined with US apathy towards reform and differing interests among the big developing countries, mean a European would probably succeed Ms Lagarde if the left the post before her term ends in July 2016.
If Ms Lagarde were to take up the European Commission role, she would have to be nominated by France, her home country.
President François Hollande has evinced little enthusiasm for doing so, in part because she is from the centre-right, not his own ruling Socialist party.
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Another concern is the risk of losing Europe's, and France's, hold on the IMF position. The IMF leadership is highly prized in Paris, which moved quickly to back Ms Lagarde's nomination when her French predecessor, Dominique Strauss-Kahn, was felled by a sex scandal. Ms Lagarde was French finance minister at the time.
"She is at the IMF, which is very important for Europe. If she leaves we won't have the IMF any more. It doesn't work. We cannot drop the IMF," said a senior official in Paris.
However, despite vigorous campaigns by emerging market candidates when the IMF and World Bank jobs last came up, current politics would likely lead to another European head if there was a selection battle.
US failure to pass reform of IMF voting arrangements means European countries still hold about a third of the votes at the fund. The eurozone crisis means it has every reason to try and keep control.
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"Following the eurozone crisis, it's very clear that the European Union needs the IMF, not just as an emergency lender but as a surveillance provider," said Domenico Lombardi of the Centre for International Governance Innovation in Toronto.
The Obama administration pushed its own candidate for the World Bank, Jim Yong Kim, signalling that it continues to subscribe to an implicit understanding that a European should head the IMF while an American leads the bank.
While the big developing countries complain vociferously about the unfairness of their candidates having no chance at the IMF and World Bank jobs, they are less united when it comes to who they want to be in charge.
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China – which is well represented in IMF management and stands to gain voting power at the fund in the long term – may prefer a European head it can influence to a strong leader from another developing country.
"Unless there are mistakes, like the Europeans nominating a bad candidate, then I think it's still business as usual," Mr Lombardi said.
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