French Finance Minister Pierre Moscovici is considered to be at the top of the list of possible successors.
Juncker, who has served for three mandates and has been the most senior politician at the monthly meeting of the 17 eurozone finance ministers, announced late Monday that he would leave the job “at the end of the year or in the beginning of next year”.
Any successor would need the support of Germany and France.
Moscovici, 55, served as European affairs minister between 1997 and 2002 in the government of Lionel Jospin. A member of the French Socialist Party, he has been elected twice as member of the European Parliament and has served as vice president of the European Parliament.
For some time, the name of German Finance Minister Wolfgang Schäuble has been circulating, but with German elections due next autumn, it appears unlikely that leaders would agree a candidate who is not certain to be part of the next government.
Senior German conservative lawmaker Michael Fuchs said on Tuesday (4 December) that Schäuble should be the next head of the Eurogroup because Germany puts up 27% of the financing for the eurozone bailout funds.
Among the other names that have been circulating is Mario Monti, the Italian prime minister who is not a candidate in the parliamentary elections due in the spring, and Jyrki Katainen, the centre-right prime minister of Finland.
EU treaties do not prevent the president of the Eurogroup from being appointed outside the select group of eurozone finance ministers. The new president can also come from outside the circle of eurozone finance ministers who make up the Eurogroup, Juncker said.
The Lisbon Treaty, in a specific protocol dedicated to the Eurogroup, says “the ministers of the member states whose currency is the euro shall elect a president for two and a half years, by a majority of those member states,” without further detail.
The new president might therefore come from the private sector or from other EU institutions, with the last option appearing the most likely.
Last year, the EU commissioner in charge of economic affairs, Olli Rehn, was tipped as the possible new chairman of the Eurogroup, but lately his name has not reappeared as a possible successor to Juncker.
Austria's Finance Minister Maria Fekter appeared to indicate that her country would insist for a prime minister to succeed Juncker.
Asked if she would want Juncker's job, Fekter said: "That's a position for a head of government and as you know I'm not a head of government. The bosses will decide how they want to handle this."
Judgment of Solomon?
The Financial Times Deutschland reported that a compromise could be found, under which Moscovici will get the job and leave it later on to be replaced by his German colleague – Schäuble or his successor.
Both Moscovici and Schäuble attended a committee meeting of the European Parliament on Monday, presenting rather diverging views on how they would strengthen the eurozone against potential attacks from financial markets.
Schäuble said that many things could be done without changing the EU treaties, and that many more would come, step by step. But he insisted on making sure not to do “the wrong thing at the wrong time” and that any major and far-reaching advance would require a treaty change. He also argued against the division between eurozone and non-eurozone countries.
Moscovici pleaded in favour of a distinct eurozone budget with “its own autonomous resource”, as well as for a special committee of the European Parliament that would act as co-legislator for the eurozone budget. He said a treaty revision was not “the first priority”, but didn’t exclude it in the long run.
The French minister also foresaw the introduction of some form of debt pooling through eurobonds or eurobills.