When President Obama names his pick to replace outgoing World Bank President Robert Zoellick, that nominee will take over an institution whose role in the global economy is becoming ever more unclear.

In part, the World Bank is a lender. But its biggest borrowers are the rapidly growing powerhouses of the developing world, countries like China and India that can arguably borrow plenty of money on their own from private investors.

The bank is also an aid donor, giving grants to some of the world’s poorest countries. But these contributions represent only a small fraction of the aid money distributed by developed countries, private groups like the Gates Foundation and other institutions.

And the bank is also an investor in private companies in emerging economies. But these investments are a drop in the sea of capital that now moves easily to places once considered too poor or too risky.

The question now is whether the bank’s new leader, who could be named in the coming days, can enhance the institution’s role at a time when developing countries are emerging as the engines of world economic growth.

“Is there a clear goal for the institution at this point in time? I would say no,” said Amar Bhattacharya, head of the G-24 Secretariat, a consortium of emerging-market and developing countries. But he added that “there is not much appetite for real major change.” An effort to recast the mission of the World Bank could set off sharp battles on its governing board, in the U.S. Congress and elsewhere.

The bank’s board has set Friday as the deadline for nominating a new president. The United States, which pledged $1.3 billion a year to the World Bank in 2011, gets to pick its leader under a long-standing “gentlemen’s agreement” that lets a European head the International Monetary Fund. The Obama administration has said it plans to nominate its own candidate to replace Zoellick — rather than, as some have suggested, holding an international competition for the post.

A small group of White House staff is heading the search, and it has not been easy.

Candidates considered a strong match for the job, such as Secretary of State Hillary Rodham Clinton and Sen. John Kerry (D-Mass.), have taken themselves out of the running. The U.S. ambassador to the United Nations, Susan Rice, has also been mentioned as a possibility. Complicating the search is speculation that both Kerry and Rice would like to replace Clinton as secretary of state if Obama wins reelection, and are thus reluctant to move to the World Bank.

Former Treasury secretary Lawrence H. Summers is regarded by some at the bank as a strong choice. But his selection would continue the string of white men who have held the top job since the bank was founded. He could also be a controversial pick because of views he expressed as president of Harvard University about the aptitude of women in the sciences.

Another possible pick, Columbia University development expert Jeffrey Sachs, has campaigned openly for the job and won endorsement from members of Congress. But he says the administration has not approached him.

Administration officials declined to be interviewed for this story. In an e-mail, a senior White House official indicated that no great change is afoot, citing general goals for the bank like “increased agility in the face of change, a focused mission and purpose, and the ability to tap into the experience and expertise now available from the growing number of countries that have succeeded in development.”

Zoellick has argued that the bank remains relevant in a changing world. Grants and low-interest loans provided through the bank’s International Development Agency are crucial for some of the 81 poorer nations who qualify for them. Investments in private projects through the bank’s International Finance Corporation, meanwhile, can determine whether riskier deals move forward. The bank can also respond quickly in a crisis, for example by setting up a special fund to offset a 2008 spike in food prices.

Zoellick suggested that “one of the problems of the World Bank is that it is called a bank.” Writing in Foreign Affairs, he said, “When it is most effective, the World Bank shares knowledge; develops long-lasting markets, institutions and capacities; and offers diverse financing.”

Less clear is whether the operation at the heart of the World Bank, the profit-making International Bank for Reconstruction and Development, is still relevant.

The IBRD was the original “world bank” set up after World War II to help rebuild infrastructure in Europe. Today, the IBRD uses its AAA credit rating to sell bonds at interest rates close to those of U.S. Treasury bonds and then lends the money it raises to creditworthy developing nations — countries such as China and Brazil.

The IBRD’s resources pale next to those of the International Monetary Fund. The bank loaned about $26 billion in 2011 , for example, a fraction of the $72 billion the IMF approved as a credit line to a single nation, Mexico.

Meanwhile, total capital investments in emerging markets from all sources have topped $1 trillion annually in recent years, and are edging back toward that level after a recent drop. By contrast, the combined net investment of the World Bank and other international development banks and agencies is estimated at less than $20 billion this year, according to the Institute of International Finance.

With interest rates for some developing nations now below those charged to European countries, it is likely that many IBRD clients could borrow elsewhere if the agency did not exist.

Given the changing nature of global finance, there’s no shortage of ideas about how the bank could also change or boost its impact beyond its current role in world finance.

Bank officials, for example, say IBRD loans aren’t just important for the money provided, but also for the technical expertise the bank brings to projects.

Bhattacharya said the bank could become more of a clearinghouse, providing expertise, oversight and information for major infrastructure projects in developing countries, even if those projects are privately financed.

Nancy Birdsall, head of the Center for Global Development, argues in a forthcoming book from Oxford University Press that the bank could become the focal point for projects to cope with climate change or other major risks to the “global commons” — and that the richer developing nations should take the lead in transforming the institution.

Without “a larger and clearer mandate,” she wrote, the bank “will gradually become merely one of many aid agencies dealing with a smaller and smaller group of low-income fragile states.”