The United States has received "positive" indications that the Saudi government will agree to a U.S. proposal to extend joint air surveillance of shipping to the lower half of the Persian Gulf, according to administration sources.

A State Department spokesman said the administration is "pleased" with talks with the Saudis to establish a second orbit over the lower gulf for the U.S. Airborne Warning and Control System (AWACS) that operates from Saudi bases.

The Saudis would provide air protection for the U.S. AWACS in the lower gulf with F15 jet fighters, as they have being doing since 1980 for those operating within Saudi territory, and monitor ship movements in the central and northern sectors of the gulf.

The extension of this system southward would allow the United States to track all ships as they enter the gulf through the Strait of Hormuz, particularly the 11 Kuwaiti oil tankers now being placed under U.S. flag protection.

It would also provide escorting U.S. naval warships early warning of any Iranian attack by motorboats, helicopters or one of the land-based Chinese-made Silkworm missiles the Iranians are installing near the strait.

"We are pleased with the discussions {with the Saudis} and anticipate positive responses from the Saudi government," said a State Department spokesman.

Another U.S. official said that while "no done deal" has been reached with the Saudis, every indication is that one will be reached soon.

Nine AWACS are now stationed in Saudi Arabia, four belonging to the United States and five newly purchased by the Saudis. The Saudis, however, are not yet capable of staffing their own AWACS.

Saudi cooperation in extending air coverage into the lower gulf appears to be the major new contribution of the Arab gulf states to bolstering U.S. military presence in preparation for the escort of Kuwaiti tankers.

Kuwait has also offered to provide free oil for U.S. warships escorting its reflagged tankers, according to U.S. officials testifying before Congress this week.

By contrast, the Reagan administration has received no new commitments from its West European allies to help protect shipping in the gulf. Defense Secretary Caspar W. Weinberger's June 15 report on security arrangements said only "a symbolic presence" on the part of the United States' European allies and possibly financial support from the Japanese were "possible."

Administration officials have been telling various congressional committees that Britain has agreed to reflag two others of the total 22 Kuwaiti-owned oil tankers.

But a spokesman for the British Embassy here said this is not precisely the case. He said Kuwait "approximately one year ago" had chartered three British-registered tankers and that Britain was not involved in reflagging any Kuwait-owned vessels.

The Arab gulf states, including Kuwait, have also told the U.S. government they will not allow Soviet warships escorting three ships the Kuwaitis have chartered from the Soviet Union to use their facilities and ports.

"This will significantly limit Soviet long-term ability to maintain or increase its current level of naval involvement in the gulf," Undersecretary of State Micahel H. Armacost told the Senate Foreign Relations Committee Tuesday.

American warships have extensive access to Arab gulf state ports, and the U.S. Middle East Force, which is being increased from five to eight, is based in Bahrain.

A senior administration official said Wednesday that U.S. military analysts had concluded that "the thing we want the most is full AWACS coverage so we don't get surprised." He said that the Pentagon has concluded it does not require "a lot of air power" to protect the Kuwaiti oil tankers and thus access for U.S. planes to Saudi airfields is not essential.

Saudi Arabia has been criticized in Congress since the Saudi failure to intercept the Iraqi jet that attacked the USS Stark on May 17 with two Exocet missiles, killing 37 sailors. It has also been criticized for refusing to allow access to its bases for U.S. aircraft that might be needed to protect the reflagged Kuwaiti ships.

The alleged lack of Saudi cooperation, heatedly disputed by U.S. officials, was one a main reason for Senate opposition to the administration's proposal to sell the Saudis 1,600 Maverick antitank missiles. President Reagan withdrew the proposal after 67 senators backed a resolution blocking the sale.

Reagan said he will resubmit the Maverick request as soon as possible. Critics have said the administration must first make the case for increased Saudi military cooperation for the Maverick sale to have any chance of gaining congressional approval.