With a little quiet encouragement from Israelis, officials in the Reagan administration are giving serious thought to an ingenious solution for one of the biggest problems in their grand design for Middle East security.

The problem is how to establish an American "strategic pressence" on the ground in a way that would deter -- or conveivably defend against -- Soviet penetrations without embarrassing the host nation and/or unnerving the neighborhood.

The solution: Smuggle it in, so to say, in the guise of a peace-keeping force to supervise compliance with the terms of the Israeli-Egyptian peace treaty.

To get some sense of just how this might work, a little background is in order onan all-but-forgotten piece of unfinished business in the famous Camp David accords. One thinks immediately of the stalled negotiations on "autonomy" for the West Bank and Gaza, now likely to remain on the back burner until after Israil's elections as the end of June.

One tends to forget that the eace treaty between Israel and Egypt, the Camp David centerpiece, had yet to be fully consummated. The Israelis have withdrawn from the largest part of the Sinai, abandoning valuable oil fields to Egypt in the process.

But the Israelis still sit on a particularly sensitive chunk of the desert -- sensitive because it contains two air bases, built by the Israelis with American help and generally considered to be the most modern in the world outside the United States. Also included is an equally sophisticated naval base at a highly strategic location, Sharm el Sheikh, on the Red Sea.

All the parties to Camp David would like to finish this final chapter in the peace treaty. For Egypt's President Anwar Sadat, there is a special urgency. Having put his prestige and influence at risk in the Arab world by signing what even the more moderal Arabs see as a "separate peace" with Israel, he is eager to receive its final fruit, the return of the last of Egypt's Israeli-occupied land.

Thus, while the "autonomy" talks are suspended, negotiations between top officials of the United States, Edgypt and Israel on completion of the peace treaty are scheduled to resume next month. On his trip through the Mideast in early April Secretary of State Haig will prepare the ground.

And according to some authorities, he will specifically raise the question of the use that might be made of the Sinai bases, not only in keeping the peace between Israel and Egypt but in the wider security interests of the area.

One hitch in all this is also, paradoxically, the reason why there exists what strikes American military planners, and some Israelis as well, as a golden opportunity. This hitch is that while the treaty calls for creating a U.N. supervisory force, the Soviets have given every indication that they would veto it in the Security Council.

It is this veto threat that has delayed the final step in the treaty. Enter the opportunity: If the Soviets continue to oppose a U.N. role, the job of supervisor of the settlement will be up for bids. That is, the parties to the treaty would be free to shop around for some sort of multinational supervisory force.

The membership of such a force would have to be acceptable to all three treaty signatories. In the case of Israel, this would exclude large parts of hostile Third World. For one reason or another, the Europeans are doubtful starters, at least without the United States.

Israeli and other proponents of the idea envisage -- ideally -- either a U.S. force alone or some multi-national combination to include friendly Asian, Latin American and African nations, with the United States very much a part of it. The theory would be that American units numbering perhaps two or three thousand, while helping eenforce Israeli-Egyptian peace, could also serve the dual purpose of maintaining a "presence," which is to say, keeping those Sinai "facilities" in a state of combat readiness as a staging area in emergencies for U.S. aircraft, even ground troops, and as a port for U.S. naval vessels.

Now comes the second hitch: Sadat, so far, has expressed adamant opposition to any military use of Sinai bases he considers "politically contaminated." Anything other than peaceful use of previously occupied territory and installations, Egyptian officials insist, would bee inviting charges of a "new" foreign occupation. Instead, Sadat is offering transient American use of Egyptian bases for pre-positioning equipment -- bases not nearly so fancy or elaborate or adaptble as those in the Sinai.

But Sadat does want the Israelis out. He is also sensitive to the Soviet threat; so are the Saudi Arabians, who would much prefer to have any American forces "over the horizon" -- but only an hour's flight away.Sadat has never been pressed as hard as Haig is likely to press him with the "strategic" argument that is the key to the new administration's Middle East approach. For all these reasons, proponents of the idea think it just might work.