Secretary of State George P. Shultz told Israeli leaders on the first stop of his Middle East tour that very slow progress is being made toward convening new Arab-Israeli peace negotiations, Israeli sources said today.

Shultz said that "the gains are being made by inches" and that four to five months may be needed to reach a decisive point, according to an Israeli participant in the talks here. The participant offered no explanation about what Shultz meant by a decisive point.

On Sunday, Shultz will hold a whirlwind round of talks with three principals in the simmering diplomacy -- breakfast in Jerusalem with Israeli Prime Minister Shimon Peres, midday meetings with Egyptian President Hosni Mubarak in Cairo and evening meetings with Jordan's King Hussein at the Jordanian resort city of Aqaba.

Shultz told the Israelis, the sources said, that although he anticipates significant discussions with Hussein Sunday and early Monday, the Jordanian monarch's trip to Washington late this month is likely to be much more important. Hussein, who will be in the United States for the graduation of his son from Brown University, is to see President Reagan at the White House May 29, officials said.

Jordanian Foreign Minister Tahir Masri said in an interview published in Kuwait today that the Palestine Liberation Organization had nominated members of a joint Jordanian-Palestinian delegation to meet with the United States on peace issues. Masri said the names have been communicated by his government to Washington, and that a response is hoped for Sunday when Shultz meets Hussein.

A senior aide to Shultz said that some names have been "tossed up" by the Jordanians on a "for instance" basis but that "we do not have in any sense a formal list" of potential participants in a U.S.-Jordanian-Palestinian meeting.

Israeli officials said Shultz did not present a list of potential Palestinian participants in his discussions with them here yesterday. Shultz spent most of today relaxing at the residence of U.S. Ambassador Samuel Lewis in Tel Aviv and holding a few informal conversations before his formal round of discussions Sunday.

In preparation for his meeting with Shultz, Hussein flew today to Jeddah to meet Saudi Arabia's King Fahd. Hussein is reported to have been unhappy that the Saudis have been unwilling to give explicit backing to his latest efforts to undertake a Middle East negotiating process.

Despite pressure from several sources, Saudi Arabia has not endorsed the Feb. 11 "framework" agreement Hussein worked out with PLO leader Yasser Arafat.

Both Israeli and U.S. officials are lukewarm about a joint Jordanian-Palestinian meeting with the United States, but neither government has ruled out such a session if it would lead to direct Jordanian-Palestinian negotiations with Israel.

An Israeli official said Shultz made it clear that he has no intention of engaging in "prenegotiations" with the Arabs on peace issues that should be taken up with Israel. At the same time, the official said, he seems willing to authorize U.S. "discussions" with an Arab delegation if the discussions would advance the peace process and if it is understood clearly that they will not substitute for the direct Arab-Israeli negotiations he is promoting.

Peres, in turn, was reported by a spokesman to oppose any U.S.-Arab meeting that would tend to "sidetrack" Arab-Israeli negotiations. But at the same time the spokesman approved as a positive step any U.S. effort that would promote direct Arab-Israeli negotiations.

Both the U.S. and Israel reject PLO participation in any set of peace talks under present circumstances. A question of intense interest and diplomatic discussion is who would represent the Palestinians in such talks and how closely tied to the PLO such representatives could be. Hussein, who has called for much more vigorous efforts by the United States in pursuit of the peace process, said in a recent interview that "American credibility is nearing its final test" in the Middle East and that "this is the last chance" for a negotiated settlement of the Palestinian issue.

Shultz is reported to have said in his private discussions here that Hussein is relatively optimistic that, despite all difficulties, his Feb. 11 accord with Arafat can open the way to full-scale negotiations. Shultz himself expressed much less optimism, at least in the short run.