Merkel has kept mum on the issue, although sources close to German Finance Minister Wolfgang Schaeuble have not concealed that he would prefer Draghi, the head of the Italian central bank, to be the next head of the eurozone central bank.
A former Goldman Sachs banker, Draghi would succeed Frenchman Jean-Claude Trichet whose appointment ends at the end of October, but this has never been said officially. France last week threw its support behind Draghi.
Speculation is rife over Merkel's silence, with media and analysts saying she wants several concessions in return for endorsing him, including on the eurozone's new bailout system, the European Stability Mechanism (ESM).
Merkel "knows that Draghi is a very good candidate but his problem is that numerous high-ranking European economic and political positions are already occupied by Italians," said Guntram Wolff, a researcher on the eurozone economy at the Brussels-based Bruegel think tank.
Her hesitation shows that "Berlin desires concessions in negotiations over Europe's permanent financial crisis mechanism, the ESM, and wants Germans in other positions," he added.
European Union leaders are haggling over a lasting bailout fund to guard against future crises in the region.
Merkel "will try to place German Deputy Finance Minister Joerg Asmussen as head of the economic and financial committee but it appears the Italian incumbent Vittorio Grilli is likely to continue presiding," said Wolff.
An article in the German magazine Der Spiegel, to be published Monday, and which does not give sources, said Merkel does not want to see Draghi appointed to the post, preferring instead that Draghi replace Dominique Strauss-Kahn as the head of the International Monetary Fund.
This despite Merkel's view of Draghi as "the most German candidate still in the race," according to Bild, another daily.
Sylvain Broyer, chief economist at Natixis, said: "The chancellor is trying to sell a German endorsement at a very high price."
Until now, her strategy of contradicting other European leaders allowed Merkel to impose her opinions, for example over the EU's "competitiveness pact" -- but that may backfire with the ECB case, he said.
Following the resignation of Bundesbank head Axel Weber in February, "without Weber and if Draghi is not taken, we risk falling again on a president who would only be Europe's lowest common denominator," said Broyer.
Business daily Handelsblatt in an editorial last week wrote that Merkel had lost her strongest trump card in the eyes of her European partners by failing to propose a credible German candidate.
Claire Demesmay, a researcher at the German Society for Foreign Policy (DGAP) said: "Berlin can no longer afford to wait."
Although Draghi's nationality works against him in "the current context of mistrust towards southern Europe, fundamentally Draghi corresponds to Germany's wishes," she said.
"He is committed to fighting inflation, which is of primary importance for Berlin."
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