THE WHITE HOUSE now pleasantly says that President Reagan may well decide next year to appoint Paul Volcker to a third term as chairman of the Federal Reserve Board. The word comes from his chief of staff, Donald T. Regan. It's a way of announcing a truce in the frequently abrasive relationship between the White House staff and Mr. Volcker.

Evidently the events of the past several weeks have reminded the White House that Mr. Volcker is extremely valuable to this administiration. He has become a powerful symbol of determination to push inflation down, and his reassuring presence at the Federal Reserve allows the administration to do and say things that might otherwise rattle the financial markets and send interest rates creeping anxiously upward.

But does Mr. Volcker want a third term? He has repeatedly said that he will stay to the end of his current one, in August 1987. Whether he decides to continue for another four years will probably depend on circumstances -- such as the character of the other board members whom President Reagan has appointed to work with him. Mr. Regan says that the recent collision within the Federal Reserve has been "blown out of proportion." To the contrary, it was a crucial and highly dangerous moment. The four Reagan appointees on the board voted to override the chairman -- an extremely rare phenomenon at the Federal Reserve and, in this case, a threat to intricate international negotiations then under way. One of the four, Wayne Angell, reconsidered and reversed his vote shortly afterward. With that the coup failed, and its leader, Vice Chairman Preston Martin, resigned from the board.

That leaves an open seat. When President Reagan decides whom to appoint, his choice will quite properly be taken as a signal of the relationship that he wishes to maintain with the Federal Reserve for the remainder of his own term.

In the famous 4 to 3 vote against the chairman, the division was not between those who want high interest rates and those who want them lower. It was essentially between the people who were following the international implications of the rates, and those who were not. Among the present board members there are only two -- Mr. Volcker and Henry C. Wallich -- who have had any substantial experience with the international monetary system and foreign economic policy. Mr. Wallich has served with great distinction, but he is now recovering from a severe illness. With the rapid decline of the dollar's exchange rate, the board's international work is currently unusually demanding.

To strengthen the board in the field in which it faces the greatest demands, President Reagan needs a nominee qualified to deal with the Federal Reserve's responsibilities abroad. All of Mr. Reagan's appointees to the board so far have been people whose interests and experience have been chiefly directed to the domestic economy. But there is another side to the board's work, and it is there that the next appointee can most usefully serve.