The Reagan administration has promised King Hussein it will act to attain a freeze of the rapidly spreading Jewish settlements on the Israeli-occupied West Bank if he declares that he intends to join Middle East peace negotiations, according to Jordanian officials and western diplomats here.

American diplomats also have signaled a willingness to accept expelled West Bank mayors as Palestinian representatives in a joint Jordanian-Palestinian negotiating team, the sources said. The United States refuses to deal directly with the Palestine Liberation Organization.

Corroboration of these U.S. offers, apparently the subjects of discussions between American officials and Hussein since his visit to Washington in December, came as this capital awaited the arrival of PLO Chairman Yasser Arafat for what are regarded as crucial discussions on President Reagan's Middle East peace initiative.

The welcome mat for Arafat rolled out Sunday, when he was expected to arrive from Tunisia. But his plane flew to Saudi Arabia, where he met with King Fahd. Expectations rose again yesterday, but Arafat was last reported in Bahrain.

Today, neither Jordanians, western diplomats nor PLO representatives here seemed certain when he would arrive, although all expected him soon. Meanwhile, there has been intense diplomatic activity here. Jordanian Foreign Minister Marwan Kasim met yesterday with Farouk Kaddoumi, head of the PLO's political department. And Saudi Foreign Minister Prince Saud Faisal flew in twice, on Friday and yesterday, bringing messages to Hussein from Fahd, according to the Jordanian news agency.

Among supporters of Reagan's initiative, there was hope that the messages indicated the backing of Saudi Arabia. Hussein has indicated that Saudi backing, along with that of the PLO, is essential for him to enter the peace negotiations.

Much of the anxiety here has found its focus in growing expressions of doubt about the U.S. role in the Middle East. Newspaper editorials and columns question American will and desire to mediate any peace settlement that would not be humiliating to the Arabs.

Much of the commentary suggests that Hussein would decline to join negotiations unless the United States provides ironclad assurances that it will act forcefully to halt West Bank settlements.

According to foreign diplomats and Jordanian officials, the Reagan administration envisions a two-step process to get the negotiations started. First, Hussein would declare his readiness to join talks. But before the king actually sat down at the table, Reagan would deliver on a promise reportedly made to Hussein during their December meeting, to have Israel freeze the settlements.

Optimists who have talked to Hussein say he is willing to accept Reagan's word that he will take meaningful action to stop settlements. But pessimists, including some of Hussein's key advisers, are urging that he get detailed guarantees of what precisely Reagan will do on settlements before taking the first step. They have expressed concern that Reagan's assurance might permit Israelis to expand existing settlements even if they refrained from building new ones. Another concern is that if Israel agrees to a temporary freeze, and the talks later break down, Israel might use that agreement to claim legitimacy for the settlements, which the Arabs regard as illegal.

Finding a formula for Palestinian representation that has the clear approval of the PLO is also regarded as critical and is thought to be one of the key topics on the agenda when Arafat and Hussein do meet. Both U.S. officials and the expelled West Bank mayors have been reluctant to put much emphasis on a reportedly common willingness to have them represent the Palestinians for fear that would backfire.

British Prime Minister Margaret Thatcher was rebuffed by the PLO when she suggested that expelled Mayor Mohammed Milhelm of Halhoul would be an acceptable alternative to a PLO official in the Arab League delegation that visited London earlier this month.

Thatcher's suggestion was "rude," one member of the PLO leadership circle said here today. "We have a structure that represents the Palestinian people"--the PLO. "How can you accept a person to represent the Palestinian people when he only represents a city?" he asked. Israel ordered the deporting of Milhelm and Fahd Kawasme, of Hebron, in 1980 on charges of having made inflammatory speeches that preceded the slaying of six Jewish settlers in Hebron.

In the end, Arafat named Walid Khalidi, a historian and a Palestinian who does not hold office in the PLO. Both the PLO and Thatcher seemed satisfied. There are hopes here that the arrangement might be the model for a Palestinian delegation that could begin a dialogue with Washington on the Reagan plan.

There is also a question of how important an agreement on Israeli troop withdrawal from Lebanon is to Hussein. Pessimists who have talked to the king say he regards that as critical. Optimists who have also seen him recently feel he is not making that an absolute precondition to declaring his intention of negotating.

A participant in the process said, "One man is going to make this deci- sion and he isn't telling. And as a re- sult, everybody is on pins and needles."