Robert Zoellick, a former Bush administration official, is believed to be ready to step down as president at the end of his term in the middle of next year.

Mrs Clinton has made clear she does not want to remain US Secretary of State, a gruelling job demanding months of world travel each year, beyond Mr Obama’s first term.

Another source said that Mr Obama supported her taking the helm at the World Bank, which is traditionally led by an American.

A spokesman for Mrs Clinton, issued a strong denial, releasing a statement saying: “Secretary Clinton has not had any conversations with the president, the White House or anyone about moving to the World Bank. She has expressed absolutely no interest in the job. She would not take it if offered.”

Discussions about the next president of the World Bank would be a natural part of talks about who should replace Dominique Strauss Kahn as head of the International Monetary Fund. The Frenchman resigned after being accused of sexually assaulting a hotel maid in New York.

The head of the IMF has always been a European and the World Bank presidency has always been held by an American, though this is now being challenged by some countries with emerging economies. The Obama administration is expected to back Christine Lagarde, the French Minister, for the IMF.