Secretary of State George P. Shultz is gearing up for a trip to the Middle East in June in another effort to promote Arab-Israeli peace talks, a U.S. official said Friday. The official, who spoke on condition of anonymity, said a final decision to make the trip is likely next week. Shultz would make stops in Israel, Egypt, Jordan and Syria, hoping to open negotiations over Palestinian self-rule and then on an overall Mideast settlement. He would fly to the Middle East at the windup of the Moscow summit meeting June 2 and then attend a meeting of the North Atlantic Treaty Organization's foreign ministers in Madrid June 9-10, the official said. Two trips by Shultz to the Middle East this year failed to produce peace talks, but the secretary refuses to give up. ``Who's afraid to struggle against odds?,'' he said at the end of the last venture in April. ``What am I saving myself for, anyway?'' He also suggested that Arabs and Israelis, despite their public lack of enthusiasm for negotiations, had privately urged him to keep trying. Shultz's first goal is a peace conference that would sponsor, but not steer, negotiations to provide some form of self-rule for the 1.5 million Palestinian Arabs who live on the Israeli-held West Bank and in Gaza. The secretary told a Senate appropriations subcommittee last week that ``under the right circumstances'' King Hussein of Jordan would be agreeable. However, he also testified that Israeli Prime Minister Yitzhak Shamir had made the conference the ``centerpiece'' of his objections to Shultz's plan. Shultz also was unsuccessful last month in Moscow in trying to persuade the Soviet Union to accept a limited role in the negotiations. Shamir _ and Shultz _ are unwilling to give the Soviets an opportunity to shape the outline of an Arab-Israeli settlement. But Hussein is insisting on Soviet involvement. On the other hand, Jordan is resisting negotiations with Israel without a guarantee that it would recover all the land it lost during the 1967 Mideast war. Shultz has advised Hussein that was not ``in the cards.'' But he backs the idea of Israel trading some territory on the West Bank for peace and said the future of Jerusalem should be decided in negotiations. Despite the long odds, Shultz said he did not think his plan was ``fated to failure.'' Shultz's plan called for a peace conference in mid-April, the opening of negotations on the Palestinians May 1 and a second stage of talks on an overall settlement beginning Dec. 1. The first two deadlines have passed. Still, Shultz has said he will keep trying to get negotiations started in the 8{ months that remain to the Reagan administration in order to give the next president a head start.