By hints and winks, and in bits and pieces, there is emerging from the Reagan administration the outline of a new approach to the Middle East. The critical innovation subordinates the regional quarrel between Arabs and Israelis to the global rivalry between the Soviet Union and the United States.

The new American emphasis is on building from the Camp David Accords between Israel and Egypt a network of security that extends to Saudi Arabia. In the interim, the Palestinians and their backers would be leapfrogged and Iran and Iraq left to stew in their own juice.

A visit to the area by Secretary of State Alexander Haig in the first week of April is the principal vehicle for the new approach. Egypt and Israel will be primary stops and the secretary will restate the administration's commitment to Camp David. He will travel in the wake of larger American arms shipments to both countries. Already under way are discussions about a base, somewhere in the area, for stationing a multinational force, including Americans.

The base will mainly be used to guarantee the Egyptian-Israeli peace as stipulated in the Camp David Accords. But it can also sited so as to provide what President Reagan, in an interview with five columnist last month, called an American "presence on the ground" near the Persian Gulf.

The most acute security problem in the Gulf is presented by Saudi Arabia.

Not that American planners expect a Soviet invasion from Afghanistan across Iran. The danger, instead, is thought to lie with elements in the armed forces, or among the foreign work force, which does most of the labor in the kingdom. Separately or together, they could set in motion a coup against the royal family.

Saudi Arabia, therefore, is another big stop on the Haig itinerary. The secretary is expected to put emphasis on the security problem. In that connection, this country is enhancing the F15 warplanes sold to the Saudis three years ago and urging them to improve their intelligence operation. There is also a view held by many Reagnites in the State, Department that in a pinch the American military could help the Saudi royals. The basic idea is for a small, highly mobile force, presumably based on Egyptian territory, that could put several thousand men anywhere in the kingdom within an hour or two.

Jordan is the other stop on the Haig tour. The United States has no immediate hopes of bringing King Hussein into the Camp David process, which in any case, is on dead center until after the Israeli elections on June 30. But the belief is that if the United States can promote understanding between Egypt and Saudi Arabia, Hussein would enter the game. In time, particularly if Prime Minister Menachem Begin is replaced by the Labor opposition, there could be negotiations between Jordan and Israel on autonomy for the West Bank Territory, which is home to most Palestinians.

Many Palestinians, especially those who look to the Palestine Liberation Organization, are adamantly against such dealing. But the PLO is currently immobilized. Two of its chief sponsors, the Iraqis and the Iranians, are at war. A third, Syria, has aligned itself with Iran against Iraq, and is isolated in the Arab world.

The Russians also oppose any accord that would bypass both them and their allies in the area. But they too have been transfixed by the conflict between Iran and Iraq. Their best bet is a falling apart of the regime in Iran that would allow them or their partisans to take over that country. But, except by giving covert and necessarily small doses of help to Iranian radicals. Moscow is obliged to keep hands off the war.

An end to the conflict, to be sure, could transform everything. But State Department planners took a long, cool look at the war in connection with the decision by the Reagan administration to support the deal cut by Jimmy Carter on behalf of the hostages. State Department officials came to the conclusion that the war was essentially an artillery duel between two gangs that couldn't shoot straight. State's best calculation is that the conflict will go on for months without either a military resolution or a political settlement. In that event, the PLO and its chief Arab supporters would continue to be immobilized.

There remain the allied supporters of the PLO cause. European countries in need of oil, notably the French and Germans, have sold themselves on the notion that Israeli accommodations to the Palestinians would yield a sure supply from the Persian Gulf. They have concocted with the British the "European initiative" that basically works to pressure the Israelis into concessions to the PLO.

But the initiative got nowhere last year. In Washington talks with allied leaders the past few days, the Reagan administration has been moving to stuff it back in the box. At the very least, there is an understanding that the allies will not push the initiative until after the Israeli elections.

Even with all these temporarily favorable conditions, a semi-miracle will be required for the new approach to work. But the try is distinctly worth-while. Success would mean a sharp tilt toward this country in the vortex of world politics. And it isn't as though the old policy was leading anywhere.