Rehn's departure from the vote of European Union ministers called by French Finance Minister Bruno Le Maire leaves just former Dutch finance minister Jeroen Dijsselbloem and Bulgarian Kristalina Georgieva, the current number two at the World Bank, left in the race.
The shortlist comprises Jeroen Dijsselbloem, the Dutch former head of euro zone finance ministers; Nadia Calvino, the Spanish economy minister; Olli Rehn, the Finnish central bank governor; and Bulgaria's World Bank chief executive Kristalina Georgieva.
The source added that France, which is leading the European selection process, had already secured Washington's support on this change.
"I withdraw my name from the ballot, so that we can achieve a broad-based consensus for the European candidate, and world-wide support", he wrote. After the vote, outgoing European Commission President Jean-Claude Juncker congratulated Georgieva on Twitter.
Britain did not field a candidate because it could not come up with a name on time, a European official said.
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.
Praised for her direct approach, she is a self-made woman who climbed the World Bank's ranks to become chief executive in 2017, after almost seven years in Brussels as European commissioner for global cooperation then for the bloc's budget. In 2016, she was a leading candidate to become United Nations secretary general before losing out to former Portuguese premier Antonio Guterres.
Georgieva, 65, has had a long career at the World Bank, the IMF's twin organization, but her candidacy would force a change in International Monetary Fund rules that require the managing director to be less than 65 years old.
Other fund members would have to make an exception for her, "which is not a given", according to one source close to the discussions. Since its creation in 1944, the fund has always been led by a European, while by convention a United States citizen is in charge of the World Bank.
A U.S. Treasury spokesman could not immediately be reached for comment on Georgieva's nomination, but U.S. Treasury Secretary Steven Mnuchin spoke highly of her work in a Reuters interview last month. She is set to replace Mario Draghi to head the European Central Bank later this year.
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