Secretary of State George P. Shultz turns to diplomatic dealings on the Middle East today after a lengthy "brainstorming" session Saturday on U.S. options and the future of the strategic region.

The immediate task for Shultz is to deal with the stalled negotiations in Beirut over the future of trapped Palestinian guerrillas and the intensified battles in the Persian Gulf following Iran's turnabout invasion of Iraq.

Both these topics are likely to be discussed by Saudi Arabia's foreign minister, Prince Saud Faisal, who arrived here yesterday and is to meet Shultz today and see President Reagan Tuesday. Saud's partner in a two-man special Arab League emissary team, Syrian Foreign Minister Abdul Halim Khaddam, is to arrive today.

The new secretary of state lifted his sights to broader horizons in a marathon session at the State Department Saturday involving former secretary of state Henry A. Kissinger and two other outsiders as well as State Department, National Security Council and Central Intelligence Agency officials.

According to official sources, Shultz announced no conclusions on operational methods or substantive policy directions, nor was there a clear statement of his next step in the search for solutions to the troubles in the area.

Reagan, arriving at the White House after a weekend in Camp David, told reporters, "George asked them the participants to come in and have a meeting and get their thoughts on what is going on."

Reagan said there had been "no decisions" about a future role for Kissinger as a special U.S. negotiator or emissary in the Middle East.

According to a participant there was no discussion of such a role for Kissinger during the session, which began with lunch in a private dining room at the State Department and continued throughout the afternoon, ending in a light supper.

At the same time nothing was said that ruled out a special function for Kissinger, who had a loose relationship with Shultz during the Nixon administration and who did much to establish the directions of U.S. policy in the region after the 1973 Middle East war.

On June 16, 10 days after the Israeli invasion of Lebanon, Kissinger wrote in The Washington Post that the fighting "opens up extraordinary opportunities for dynamic American diplomacy throughout the Middle East," especially in creating an opening to overcome the obstacles in the deadlocked negotiations on Palestinian autonomy in the West Bank and Gaza.

More recently Kissinger has been critical of the U.S. role in the current Beirut negotiations and especially of the plan to send U.S. Marines to help police the withdrawal of Palestine Liberation Organization guerrillas.

Informed sources depicted Saturday's meeting as an intellectual exercise in keeping with Shultz's professorial instincts and inquiring mind, and highly unusual for the top rank of government.

The presence of three private citizens--Kissinger, former government official and diplomat Laurence Silberman, and retired industrialist Irving Shapiro--reportedly helped to keep the discussion focused on basic factors in the Middle East, including emerging relationships and problems between the United States and Israel, the Palestinians and other Arabs, rather than on immediate decisions.

Shultz is reported to have done much more listening than talking, although his clear and specific questioning is said to have helped sharpen the views of the participants.

It would be a surprise to those involved in the exercise if Shultz were to quickly decide and announce major changes in U.S. policy.

According to United Press International, Reagan has convened a National Security Council meeting for today with the Middle East at the top of the agenda. Also participating in Saturday's State Department session were Deputy Secretary of State Walter J. Stoessel, Undersecretary of State Lawrence S. Eagleburger, Assistant Secretary of State Nicholas A. Veliotes, director of policy planning Paul D. Wolfowitz, special Mideast negotiator Richard Fairbanks, deputy NSC director Robert C. McFarlane and CIA specialist Robert C. Ames.

Shultz left the session at times for other meetings, including separate sessions with Israeli Ambassador Moshe Arens and Egyptian Ambassador Ashraf Ghorbal.

Official sources said Shultz is hoping to recruit Kenneth W. Dam, provost at the University of Chicago and a longtime colleague, to become deputy secretary of state, replacing Stoessel. Dam worked closely with Shultz in the Nixon administration and the two men wrote a book on economic issues in 1977.