The State Department's top-ranking Middle East expert, Assistant Secretary of State Richard W. Murphy, will visit Saudi Arabia, Syria and Israel, probably beginning this weekend, as the Reagan administration seeks to revive the Arab-Israeli peace process in the wake of the unrest sweeping the West Bank and Gaza Strip.

Department spokesman Charles E. Redman did not give a date for Murphy's trip and listed only Syria and Saudi Arabia as his destinations. However, informed sources said Murphy expects to leave Friday. The sources added that at a meeting yesterday with Israeli Ambassador Moshe Arad, Murphy agreed to stop in Jerusalem to inform Israeli leaders of the reaction in Damascus and Riyadh to the new U.S. proposals.

The sources also said that Philip C. Habib, a special U.S. envoy who presented the proposals to Jordan's King Hussein last weekend, described the king's reaction as "generally positive and receptive" to the evolving American initiative. That was in contrast to public statements by Hussein in Paris yesterday criticizing the United States for failing to condemn Israel's actions in the West Bank and Gaza.

However, the sources noted, Hussein essentially talked around the question of whether he would welcome a new U.S. initiative. Asked for his reaction to Habib's visit, the king said: "We will have to wait and see what happens."

The sources described Hussein as feeling it is far too early to commit himself to any process that might lead to direct negotiations with Israel over the future status of the occupied territories with their 1.5 million Palestinian inhabitants. But, the sources added, Hussein reportedly told Habib that the initiative has possibilities that merit further discussion.

Although Redman declined to discuss details of the U.S. plan, its outlines envision U.S.-mediated, indirect talks among Israel, Jordan, Egypt, Palestinian leaders and any other Arab countries willing to join the process on electing a self-governing authority in the territories by September. Next, direct negotiations among these parties would begin in December on the permanent status of the territories, occupied by Israel since 1967.

U.S. officials privately concede that the initiative is, at best, a long shot that must overcome formidable hurdles for any hope of success.

The most immediate problem involves finding a way for Hussein to abandon his two-decade refusal to deal directly with Israel over putting the territories under Jordanian control. The king, who fears being isolated within the Arab world and branded a traitor to the Palestinian cause, has insisted that any talks must take place at an international conference, lending him the legitimacy of multinational backing.

However, Israel's ruling coalition last year rejected this approach.

Hussein also has shown uneasiness in the past about whether bringing 1.5 million Palestinians under the Jordanian flag would undermine his hold over his small country, and sources say there are signs that the violent rioting in the territories may have rekindled his doubts.

Sources say the United States hopes Hussein will conclude he could demonstrate to West Bank and Gaza inhabitants that he, not radical, terrorism-oriented groups like the Palestine Liberation Organization, offers the best hope for winning limited Palestinian self-rule and eventual freedom from Israeli occupation.

Should Hussein enter the process, the next big problem will center on whether the two dominant groups in Israel's coalition government -- Yitzhak Shamir's Likud bloc and Shimon Peres' Labor Party -- can agree on a format for direct talks acceptable to Jordan, or compromise their contradictory views about the territories to achieve a unified Israeli negotiating position.

The dominant factions of the Labor Party favor a "land for peace" formula of surrendering the territories in exchange for Arab recognition of Israel's right to exist. The Likud position has been that the West Bank, for strategic and historic reasons, should be absorbed into Israel.

Israeli sources noted that Shamir, under fire from hard-line Likud elements for agreeing to drop its longstanding insistence on a lengthy autonomy period, could be in danger of losing his control over the party if his gestures are seen as moving closer to Labor's position.

Lastly, there is the problem of finding Palestinians willing to serve in the proposed self-governing authority. In addition to the threat of PLO assassination, the situation in the territories is so volatile that moderate, pro-Jordanian Palestinians face a variety of potential new dangers if they are seen as puppets or collaborators with Israel. Thus it is unclear that Palestinians acceptable to all sides can be convinced in the current atmosphere that they have an opportunity to gain the autonomy and perhaps ultimately the independence that has eluded them for 20 years.