Prime Minister James Callaghan will urge President Carter next week to join in a five-nation plan to halt the slide in the dollar, authoritative sources disclosed yesterday.

The Prime Minister and his aides have sketched out a blueprint for currency stabilization that embraces West Germany, Japan, France, Britain and the United States-the world's dominant trading nations. The opening of talks on this scheme, it was learned, is the prime reason for Callaghan's hurriedly arranged trip to see Carter in Washington Thursday.

Unless concerted action is taken to stop the fall in the dollar's exchange rates, Callaghan fears, the upheaval in the world's monetary system could result in economic and political disaster. But if the five countries agree to check the decline, he argues, the stabilized rates would hold because there is no other currency into which billions of speculative and investment dollars can be exchanged.

Details of the mechanism to stabilize the dollar and its exchange rate in yen, marks, pounds and francs will be left open to negotiation. Callaghan hopes that a final agreement can be reached before the July economic summit that will bring together non-Communist leaders in Bonn.

The heart of the plan calls for a declration by the five governments that their central banks will buy and sell dollars within some limited range. For example, if dollars flow out to buy Volkswagens, the West German central bank will pay the German manufactuer something more than twomarks for each dollar he cashes. In the same way, British Airways, carrying American tourists to London, would receive from the Bank of England less than 50 pence for every dollar paid to the airline.

Any losses or gains incurred by the central banks would be shared equally among the five. Thus, if the market rate for yen was higher than the price paid by the Japanese central bank to the Sony Corp., Tokyo could call on its four partners to share the exchange loss.

Callaghan and his advisers are convinced that any exchange profits or losses would be negligible compared with the enormous advantages of stabilizing the currency around which the world monetary system revolves. In any event, the British believe there will be virtually no gains or losses because market rates will have to reflect the range agreed on by the central banks.

In effect, Callaghan will try to sell Carter on a currency snake among the five most important currencies. In the British. view, currency markets are not genuinely free and can be dominated-at least for a while-by the concerted action of the five big central banks.

The aim is not to freeze relationships between the five currencies indefinitely. The British think that is unrealistic because nations grow at different rates suffer from different rates of inflation and swing separately from surplus to deficit in their balance of payments. The proposal is viewed here as a short-term measure to avert a possible imminent disaster.

Without common action to halt the dollar's fall, the British believe, the major central banks will follow the Swiss example and simply refuse to take in dollars at all.

This, it is feared, could lead to the erection of even higher walls against imports, disrupt trade, convert the present weak expansion in the world economy into a depression and increasingly higher unemployment.

Callaghan will argue that the falling dollar is not merely a problem for Japan and West Germany, the two nations whose currencies have appreciated the most and whose exporters find their prices steadily rising in American markets.At one time, Washington took the position that dollar depreciation was a largely European concern.

The prime minister will contend that British experience demonstates that a depreciating currency abroad undermines the value of a currency at home. As Volkswagen prices rise in dollars, the argument goes, General Motors Corp. will be freed of a competitive restraint and Detroit's car prices will float nearer the German level.

Callaghan sounded out West Germn Chancellor Helmut Schmidt last Sunday on his dollar stabilization scheme. The British say Schmidt showed interest in the objective but how deeply the pair went into a working mechanism is not known.

The dollar plan is the most urgent but not the only project Callaghan will put before Carter. In addition, the prime minister intends to discuss:

A long-term scheme to insure that nations with payments surpluses like Japan and West Germany channel their excess funds into deficit countries like the United States concerted management of surpluses and deficits to ward off deflation has already been proposed publicly by Harold Lever, chancellor of the Duchy of Lancaster and Callaghan's chief economic advisor in the cabinet.

Common measures to deal with problems of energy, growing trade protection and the slow economic growth in the non-Communist world.

The Callaghan proposal like all foreign policies, reflect domestic imperatives. A warning from the British Treasury that a substantial tax cut planned by Callaghan for April would depress the pound and hurt the U.K. payments balance by increasing imports led to the proposal sources said.

The realization that the tax cut will have to be smaller than planned originally because of the worrisome world economy gave Callaghan and his economic advisers added impetus to come up with something new.