The moderates of the Arab world - in particular Jordan - are eager for any diplomatic initiative that removes the West Bank and Gaza from Israeli control and makes a move toward resolving the decades-long statelessness of the Palestinian people.
This seems especially so in the wake of Israel's invasion of Lebanon and the weakening and scattering of the Palestine Liberation Organization.
Israel's ever-tightening grip on the West Bank and Gaza and its frequent declarations that there already is a Palestinian state in Jordan have been troubling for King Hussein and his brother Crown Prince Hassan. The Jordanian royal family has been pressing since 1981 the Reagan administration to find a way of freezing Israeli settlement of the West Bank and Gaza and ultimately ending Israel's 15-year-old control of these territories.
Yet, despite initial Jordanian interest in President Reagan's Palestinian initiative this week, there are many reasons why Jordan may have a difficult time taking the lead role that the Reagan plan envisions.
Two of the most important of these reasons are the PLO and Syria.
Though King Hussein proposed a plan similar to President Reagan's in 1972 (the ''United Arab Kingdom'' - a two-state federation, Palestinian on the West Bank, Jordanian on the East Bank), the 1974 Arab summit conference in Rabat, Morocco, removed from the monarch the Arab League's sanction to negotiate for the Israeli-occupied territory.
Since that time, the PLO has been designated the sole ''legitimate representative'' of the Palestinian people. Since that time also, King Hussein - while maintaining extensive working contact with West Bank Palestinians - has been very careful not to give the impression he wanted to usurp the PLO.
This attitude stems from the King's recognition that, unlike Egypt under Anwar Sadat, Jordan is too vulnerable to go against the wishes of the PLO and the Arab world.
Moreover, during the past decade, West Bank political leaders have gravitated , if not always toward the Beirut-based PLO, more toward political self-reliance than towards Amman.
For Jordan again to take the negotiating lead toward the occupied territories , the PLO and the Arab League would have to give their blessings. And that does not seem likely.
The PLO, anxious to reassert itself in the Arab world after forced exit from Lebanon and dispersal of its guerrillas, would be reluctant to hand over its right to negotiate on behalf of the 3.8 million Palestinians to Jordan. To do so would effectively end the PLO's diplomatic as well as its military reasons for existence.
Syria and the radicals of the Arab Steadfastness and Confrontation Front (Libya, Algeria, South Yemen, plus the PLO) also present problems.
Because it harbors the most radical of the PLO and because it is deeply at odds with the Jordanian monarchy, the Syrian regime will not endorse a lead role for Jordan in peace talks with Israel.
On Sept. 2, the Popular Front for the Liberation of Palestine, a Marxist PLO faction now based in Damascus, flatly rejected Mr. Reagan's initiative, saying it was simply ''a new maneuver aimed at improving America's image in the Arab area and facilitating the mission of reactionary Arab regimes at the forthcoming Arab summit.''
''Reactionary Arab regimes'' is a phrase aimed at countries that did not help the PLO fight against Israel in Lebanon this summer. Among these were Saudi Arabia, Jordan, Iraq, and the Gulf states. But not Syria.
Syria put up a stiff, if unavailing, fight against Israel in Lebanon this summer - and a future Syrian-Israeli struggle for eastern Lebanon, in which the PLO is still active, looms.
Because such a statement was broadcast from tightly controlled Damascus it can be seen as also reflecting the sentiments of the regime of Syrian President Hafez Assad. (The statement not only bodes ill for the Reagan plan but also for the reconvening of the Arab summit in Fez, Morocco, Sept. 6. If Arab radicals decide not to go the summit will collapse just as it did last year.)
Seeing his country now as prime protector of the PLO, Mr. Assad could very likely take it upon himself to prevent King Hussein from ''selling out'' the PLO by negotiating toward a West Bank under Jordanian control.