The IMF managing director has said she is "open" to seeking another term when her time is up in July 2016, while the so-called BRICS -- Brazil, Russia, India, China and South Africa -- seem divided about a power bid.
Questioned by AFP, Moscow and Brasilia refused to comment. But Pretoria seems to be already gearing up to contest the European leadership of the 70-year-old IMF, part of the tacit agreement with the United States that has kept an American as head of sibling institution the World Bank.
Though the complaint is not new, it has failed so far to produce change.
In 2011, the BRICS were unable to agree on a single candidate who would convey undeniable symbolic clout, leaving Mexico's Agustin Carstens to pursue a losing battle against Lagarde.
It is an open question whether that would be different today.
"It's too early to say. Let the situation become clear, which other candidates are in the race," said an official at the Indian finance ministry.
Hua Chunying, spokeswoman for the Chinese foreign ministry, was circumspect. "China has been in a good, sound, cooperative relationship with the IMF," she said.
Since 2011, however, the situation has changed.
The five big emerging-market economies have strengthened their cooperation with a constant goal in mind: to challenge the West's grip on the Bretton Woods sibling institutions by creating their own monetary fund and development bank.
They chafe at their underrepresentation at the IMF, where the voting rights of China, the world's second-largest economy, are not even a quarter of the United States.
Cracks have appeared within the 188-nation IMF itself. In July, the institution's number-two official, David Lipton, told the BBC that it was "much more likely the next time around than it has ever been" that the next IMF chief will be a non-European.
The prospect of a common BRICS candidate, however, faces a number of obstacles, according to experts interviewed by AFP.
The choice of a candidate, for starters. A former IMF chief economist who currently heads India's central bank, Raghuram Rajan, has the ideal profile but he himself has torpedoed speculation.
