Four people remain in the running after Portuguese Finance Minister Mario Centeno dropped out, and Brexit-bound Britain decided not to field a candidate, the ministry said.
French Finance Minister Bruno Le Maire is leading the effort to find common ground on the EU's pick to head the Washington-based global lender, which by tradition is led by a European.
The vacancy came up after the current IMF chief, Christine Lagarde of France, was nominated to become the next head of the European Central Bank following the end of Mario Draghi's term.
But there has been no consensus on a candidate, reflecting deep divisions in the European Union over the IMF's role during the financial crisis beginning in 2008.
Nations in southern Europe have long memories of the tough austerity measures imposed as part of the IMF-backed debt bailouts, which they say choked off the economic growth they badly needed to recover.
Northern countries, for their part, worry that southern European candidates lack sufficient experience and would not insist enough on reforms needed to rein in spending and deficits.
The four candidates are Spanish Finance Minister Nadia Calvino, former Dutch finance minister Jeroen Dijsselbloem, Bank of Finland chief Olli Rehn, and the World Bank's second-in-command Kristalina Georgieva of Bulgaria.
Southern countries chafe at the prospect of a Dijsselbloem candidacy because of his tough stance against nations like Greece when he headed the group of EU finance ministers.
"I can't spend all my money on drinks and women and then ask for help," he said in one particularly notorious comment in 2017.
Under the EU's qualified majority voting rules, the winner will need the backing of at least 16 of the bloc's 27 member states, representing at least 65 percent of its population.
"Several rounds of voting will be organised if necessary," the French finance ministry said.
The IMF plans to select its new leader by October 4. Since its creation in 1944, the fund has always been led by a European, while by convention an American is in charge of the World Bank.