THE WHITE HOUSE is wasting time over the choice of the next World Bank president as though it didn't make any difference, but the World Bank is crucial to the plan that the secretary of the Treasury, James Baker, has proposed for dealing with the Latin debts. If the delay over the appointment continues, Mr. Baker will eventually begin having difficulty persuading the rest of the world that the White House is prepared to give his plan active and vigorous support.

It has now been more than three months since the World Bank's current president A. W. Clausen, said that he would not seek reappointment when his present term ends in June. He made the announcement, incidently, at the same meeting in Seoul, Korea, and on the same day as Mr. Baker's address outlining the Latin debt plan. Since then, inevitably, Mr. Clausen has become something of a lame duck at the bank, and the bank itself has been losing momentum.

But the Baker plan's emphasis on the World Bank is loaded with significance for the Latin borrowers. Of the two great international lending institutions that face each other across 19th Street, governments and commercial banks concerned with the Latin debts have so far been mainly working through the other one -- the International Monetary Fund. Because the IMF's job is to deal with the foreign exchange emergencies, its remedies tend to be addresssed to the short run, and because balance-of-payments trouble usually involved overspending they tend to begin with restraint and austerity. Mr. Baker's references to the World Bank were a signal to Latin America that the United States is prepared to take a longer perspective in dealing with the debts and, instead of austerity, it wants to rely more heavily on economic growth to balance accounts. To Latin America, that is a highly welcome change.

But the Baker plan has never been spelled out in any great detail. For example, the World Bank has the funds to maintain its role for only perhaps a couple of years. What happens then? The Reagan administration has never been enthusiastic about expanding the international banks' resources, and Congress has never voted them money without a long and onerous struggle.

In formal terms the next president of the World Bank will be chosen jointly by all the governments that belong to it. But tradition holds that the nominee will be an American, and as a practical matter, he will be named by the Reagan administration. Who should it be? Clearly, it needs to be a person of sufficient international standing to have the confidence of both the Latin Americans and the commercial bankers. It needs to be a person of sufficient breadth to speak to the large issues of fairness and social justice raised by the repayment of the debts. It has to be a person capable, here in Washington, of coaxing further support from a Congress laboring under the shadow of Gramm-Rudman.

It would be reassuring to think that the White House was energetically searching for the right candidate. But there are no visible signs of it.