When Issam Sartawi, an adviser to Palestinian leader Yasser Arafat, said in Paris last week that the PLO is ready to recognize Israel "on a reciprocal basis," many Middle East watchers pricked up their ears to listen for a possible change in the standard Middle East equation of mutual obliteration.

But despite this and other vaguer hints that something large was in the offing, Palestinian and Arab sources here and in Beirut say that mutual recognition between the PLO and Israel is as unrealistic an immediate goal as ever.

Instead, they say, what the PLO and its Arab backers now want, in exchange for an orderly departure from Beirut, is an indication by Israel's principal supporter, the United States, that it has begun, even if just a little, to see the overall Palestinian problem the same way they do.

"We want American recognition," an aide to Arafat said in Beirut yesterday. While other Arab leaders have not said it as bluntly, statements during the past week have implied that it is to Washington, rather than Tel Aviv, that they are looking for a sign that the Palestinians may be one small step closer to the long-term goal of having a state.

The opportunity for such a sign, they say, will come early this week when the foreign ministers of Saudi Arabia and Syria arrive here in a joint delegation for talks with President Reagan and other administration officials.

As little as three weeks ago, the PLO seemed in no position to make demands, or even suggestions. Militarily defeated, cornered in West Beirut and the subject of negotiations in which it had little say, its choices appeared limited to suicide, surrender or expulsion. There appeared to be little consensus in the rest of the Arab world on what to do in response, and little stomach to do much of anything.

But in the meantime, these sources say, the world and Washington once again have grown weary of seemingly endless war in the Middle East, and have had time to reflect on the extent and method of the Israeli sweep through southern Lebanon and the continuing siege of West Beirut.

The Arabs have had an opportunity to work toward tidying up their own disarray during the weeks-long Israeli pause--attributed by one Arab spokesman to Israeli squeamishness--on the outskirts of the Lebanese capital. "Blitzkriegs only work for 'true' fascists" who are prepared to go the limit without hesitation, Arab League Ambassador Clovis Maksoud remarked.

Now, in addition, the United States has a new secretary of state.

Although the PLO appears to have agreed to leave Beirut, sources say it and the Arabs now believe they can ask for, and stand a chance of getting, an American quid pro quo. According to Washington Post correspondent William Branigin in Beirut, specific PLO demands center on some form of U.S.-PLO arrangement to put the Palestinian guerrilla departure in the context of a package deal that would advance the cause of recognition of the PLO and Palestinian self-determination.

Depending on which Palestinian official one speaks to, Branigin reported, the U.S. part of the bargain could be as little as receiving PLO representative Khalid Hassan, now in New York, as part of the Saudi-Syrian delegation. French and British leaders last week both received PLO "foreign minister" Farouk Kaddoumi as part of a similar delegation.

A U.S. move could extend to American insistence on PLO participation in the Middle East peace process as one of the representatives of the Palestinian people, or even, at its most unrealistic limits, to the recognition of the PLO as the Palestinians' sole legitimate representative.

Another option reportedly under Arab and PLO discussion is U.S. support for a new United Nations Security Council resolution that would effectively amend Resolutions 242 and 338, which call for recognition of the rights of Palestinian refugees, Israeli withdrawal from occupied territories, and Israel's right to live within secure boundaries. A new resolution would mention the rights of the Palestinian people as a whole. The United States opposed a similar proposal in 1977, but drafts of a new French resolution, which some sources say specifically mentions the PLO, reportedly are now being reviewed in Paris, Washington, Moscow and other capitals.

Whether the Arab League delegation will make proposals that specific is doubtful. Rather, Maksoud said in an interview here, the delegation is coming because "we see some window of opportunity"--that if Arab objectives are not U.S. objectives, "at least now they are U.S. concerns."

Maksoud echoed PLO officials who had singled out former secretary of state Alexander M. Haig Jr. as the principal architect of U.S. support for the Israeli invasion and expressed pleasure at the statement by his successor, George P. Shultz, in confirmation hearings last week. In an unprecedentedly direct paraphrase of moderate Arab dogma about the proper focus of Middle East priorities, Shultz said that it is "painfully and totally clear" that the "legitimate needs and problems" of the Palestinian people must be resolved.

Should the administration in fact be ready for a policy change on the Middle East, something that is not at all clear at this point, its question undoubtedly will be what the PLO and its principal Arab backers are willing to give in return.

Most immediately, sources said, the Arab delegation could offer the peaceful evacuation of 5,000 to 6,000 PLO fighters now surrounded in West Beirut. Although Syria has refused thus far to accept the guerrillas, it is believed to have its own agenda for what could make such an arrangement more attractive, including forcing both the Saudis and the United States to take Damascus more into account in the Middle East in general.

But the question of mutual recognition is likely to hang in traditional limbo.

In response last week to Sartawi's statement on mutual recognition, a State Department spokesman said, "The United States will not recognize or negotiate with the PLO so long as the PLO does not recognize Israel's right to exist and does not accept Security Council Resolutions 242 and 338."

The Arabs consider the recognitions/resolutions question a straw man. Despite a history of rhetoric and action to the contrary, "it has been understood," Maksoud said, that the PLO is willing to recognize Israel and let it live in peace in exchange for Israeli recognition of the PLO and the Palestinian right to a homeland and a state.

For years, PLO recognition of Israel's right to exist has been Arafat's "trump card"--the one to be held close to his chest, always with the hint that it could be used, but only if it would win the game. Rather than demanding all of what it considers Palestine, the implied corollary to this willingness has been acceptance of such a state within the bounds of the Israeli-occupied West Bank and Gaza Strip.

Israel's lack of responsiveness to "implied" recognition and its corollaries has its own basis in a history of PLO radicalism and violence and in Menachem Begin's declared biblical and national security rights to all of Palestine.

There are some who believe that the time has now come to begin calling bluffs, and for the PLO to issue a unilateral, public statement of willingness for mutual recognition with Israel. By some interpretations, most notably his own, Sartawi's statement in Paris last week was just that.

In today's issue of the Lebanese English-language weekly Monday Morning, Sartawi was quoted as saying in a telephone interview from Paris that the United States should "fulfill its obligation" and recognize the PLO now that the PLO has recognized Israel's right to exist.

One PLO source in Beirut pointed out that the original statement was repudiated neither by the mainline PLO nor its more radical fringe groups. This source said Sartawi's statement evidently was "authorized" and aimed at drawing positive response from Britain and France. "It's part of a delicate minuet," the source said.

Others, however, acknowledge that there is no really serious talk about mutual recognition.

Most important, the issue has shifted, at least in part, from the siege of Beirut to rest where the PLO and the Arabs always have wanted it--on the Palestinian question as the key to the problems of the Middle East.