DAMASCUS, SYRIA, FEB. 26 -- The Syrian leadership, which harbors perhaps the lowest of Arab expectations that a new U.S. Middle East peace initiative can produce positive results, is nonetheless basking in the recognition that Saturday's visit of Secretary of State George P. Shultz confers on Syria's influence in the region.

Just six months ago, a visit of an American secretary of state to this country would not have been possible in the wake of U.S. sanctions against Syria for its alleged involvement in a plot to blow up an Israeli jumbo jet two years ago.

The Shultz mission here follows exploratory trips last July by the U.S. ambassador to the United Nations, Vernon A. Walters, and earlier this month by Assistant Secretary of State Richard W. Murphy. Ambassador William L. Eagleton Jr. returned here last September after being recalled because of the Israeli airliner incident.

As Shultz leaves Tel Aviv with little more than a restatement from Israeli Prime Minister Yitzhak Shamir that Israel remains opposed to an international peace conference, there is scarce new business to place on Shultz's agenda for the two hours he is expected to meet with President Hafez Assad, Arab and western officials here said.

But the Syrians are treating Shultz's visit as a sign that the United States, still considered the most influential superpower in the region, has recognized that no comprehensive solution can be negotiated without Assad's participation.

"The Syrians like to be consulted. They expect to be consulted," said a senior western diplomat.

Shultz's last, ill-fated visit here was on July 6, 1983, when he tried to salvage an agreement brokered by the United States and Israel for the withdrawal of Israeli troops from Lebanon. Syria was excluded from negotiations prior to the agreement, which called for joint Israeli-Lebanese supervision of security arrangements in southern Lebanon, and Damascus backed a revolt by Lebanese Moslems in early 1984 that led to Lebanon's abrogation of the accord.

The Lebanon disappointment, the bombing of the U.S. Marine barracks in Beirut in October 1983, Syria's downing of two U.S. warplanes in late 1983 and its capture of one U.S. crewman, and the withdrawal from Beirut of U.S. forces after the Moslem revolt helped strengthen Assad's reputation as the potential "spoiler" of any Middle East initiative that Syria opposes.

That reputation remains today, though Syria's capacity to exert its power has been diminished by economic problems, a costly military deployment in Lebanon and an elusive aspiration to achieve strategic military parity with Israel.

Still, said one western official, "the Syrians can afford to be tougher." Unlike Jordan, Syria does not live with the constant threat of destabilization from a large Palestinian population, nor does it face the same threats by the Israeli right to push the 1.3 million Palestinians of the West Bank and Gaza Strip into its territory as a militant solution to the Palestinian problem.

Shultz, who was deeply frustrated by the failure of U.S. policy in Lebanon, will meet Assad at a time when Syria's traditional hard line and legendary intransigence in the Arab-Israeli dispute does not weigh heavily in American diplomacy. Israel's internal political deadlock continues to leave frozen the question of a comprehensive solution to the future of the Arab territories occupied by Israel in the 1967 Arab-Israeli war and the Palestinian question.

Western sources here have said Syrian officials are suspicious that the American mission to the Middle East is an attempt by the Reagan administration to divert world attention from the Palestinian uprising in the West Bank and Gaza Strip and to give the Israelis more time to put it down.

Commentary in the state-controlled media here has included the usual harsh rhetorical accusations that U.S. policy in the Middle East is guided by Israeli interests.

Yet some western officials say they have detected a softening of the rhetoric in the final days before Shultz's arrival. Syrian officials have been treating the Shultz visit "almost as if they are interested in what Shultz might bring and not just rejecting it out of hand," one diplomat said.

For Assad, the meeting with Shultz is likely to include a long and careful recitation of Middle East history from the Syrian perspective. But western sources said Shultz will be seeking clarification of Syria's conditions for negotiating with the Israelis in some kind of international forum.

Jordan's King Hussein told American officials last spring that he had won Assad's commitment to join an international peace conference under terms that Hussein had worked out with Israeli Foreign Minister Shimon Peres. But after Peres failed in his attempts to win Israeli Cabinet backing for the conference, Assad has retreated from discussing the issue in anything but vague terms, western officials have said.

The return of the Golan Heights, lost to Israel in 1967 when Assad was Syria's defense minister, remains one of Syria's goals in a Middle East peace settlement.

Shultz's statement at the outset of his journey here that the return of Golan must be addressed in any comprehensive settlement will certainly play well in Damascus.

"I don't think anybody expects this round of talks to provide any definitive position on anything, and no one is going to give a definitive yes or a definitive no," a western official said.