Other candidates include François Villeroy de Galhau, a governor of the Banque de France; Olli Rehn, a governor of the Bank of Finland; and Erkki Liikanen, a former governor of Finland’s central bank. None have been campaigning as vividly as Mr. Weidmann, 51, who has been softening his tone and trying to shed his reputation as a hard-liner.

Selling the euro is essential

Decisions on monetary policy are made by the central bank’s Governing Council, which with 25 members is more than twice as large as the Federal Open Market Committee that sets monetary policy in the United States. The president of the European Central Bank has only one vote. But he — no women have been mentioned as candidates — leads the council’s meetings, answers questions from reporters after monetary policy meetings, and can move markets with his public statements because of the tremendous weight that investors place on a central bank president’s every remark. And when markets are on fire, he must find the words to stop the panic.

The central bank president, although not an elected official, needs political skills to sell the euro to a sometimes skeptical public and to withstand attacks from populists and people who never wanted a common currency and would still like to have their deutsche marks, francs or liras back. Mr. Draghi, who spent a decade earlier in his career as the Italian Treasury’s highest-ranking civil servant, knew how to keep functioning in the middle of political chaos. People still call him “maestro.”

“Draghi’s successor will be an essential figure in determining how much further the E.C.B. would be willing to go if it were to face another systemic crisis,” Mr. Talavera of Oxford Economics said.