A. w. (Tom) Clausen, president of the Bank of America, the nation's largest bank, was proposed yesterday by President Carter to become the next president of the World Bank, succeeding Robert S. McNamara.

Clausen, 57, is regarded as a conservative banker, with considerable international experience.

His appointment to a five-year term beginning next June must be approved by the bank's board of executive directos representing the 138 member-countries of the bank. However, in practice, directors traditionally accept the selection of the U.S. president.

The Carter administration began telling representatives of key nations in the bank that Clausen was among the final candidates, and spent the past two weeks advising them that he was to be Carter's choice. According to admnistration officials, the finalists included Anthony Solomon, head of the Federal Reserve Bank of New York, Peter Peterson, former secretary of commerce and now a New York investment banker, and Paul W. Volcker, chairman of the Federal Reserve Board.

Clausen won a ringing endorsement from George Shultz, treasury secretary in the Nixon administration and now a top economic adviser to Republican presidential candidate Ronald Reagan. "Tom Clausen is a first-class banker," he said yesterday. "He knows the opportunities as well as the problems to be addressed in developing countries."

Clausen said in an interview that he doesn't quarrel with the label "conservative." That's an attribute, he said. The World Bank must rely on its reputation, he said, and "it's not in its best interest to have a reputation for throwing money down a rathole and making impossible loans that can't be repaid. On the other hand, being conservative doesn't exclude being sensitive to what is required and having a commitment to try and find solutions."

The challenge facing the World Bank "of keeping the lesser developed countries alive so we can effect long-term cures is challenging and I think the next few years will be critical," he said.

Administration officials said Clausen's selection was applauded not only by foreign governments, but also by close advisers of Reagan and other leading Republicans.

Clausen's standing among Third World countries was a major factor in his selection, administration officials said.

His standing in the Carter administration is high. At least twice before, Carter was prepared to offer him the post of secretary of the treasury.

Clausen would take over as the World Bank faces a host of economic and political problems. McNamara, in his last speech to the bank's annual meeting last month after serving as its president for 13 years, called for a massive increase in the bank's lending capacity to enable it to meet the challenges of the 1980s. Slow growth in the industralized world and the soaring cost of energy have worsened the problems of the world's poorest nations. The bank committed $12 million last year to help finance development projects.

Clausen joined the Bank of America as a trainee just out of the University of Minnesota law school and rose to become president of the San Francisco-based institution 20 years later in 1970, at the age of 47. His age was a plus in the eyes of the administration's selection team because he is young enough to serve more than one five-year term as the bank's head.

Clausen's career at the bank included key roles in the bank's expansion in the United States and in foreign countries. Last year, the bank's assets reached nearly $110 billion and the bank's prominence in international banking has grown increasingly under Clausen's direction.