King Fahd of Saudi Arabia was reported by authoritative diplomatic sources here to have sent a private message to Soviet leader Yuri Andropov. It was the first known Saudi approach of this kind in decades.

In his message, which is said to have been relayed to Moscow via Kuwait, the king raised the questions of the Iranian-Iraqi war and falling world oil prices, according to Arab diplomats.

It was not known whether Andropov had responded to the Saudi communication, which was said to have been relayed four to six weeks ago.

The Soviet Union and Saudi Arabia do not maintain diplomatic relations, and their contacts have been confined to annual exchanges of congratulatory telegrams on their respective national days.

Diplomatic analysts here said Fahd's message may have been a part of the atmospheric thaw between the Soviet Union and Saudi Arabia that began with the visit to Moscow last December of Prince Saud, the Saudi foreign minister. The analysts emphasized that they did not expect a resumption of Soviet-Saudi diplomatic relations in the foreseeable future.

Saud, who was a member of an Arab delegation led by Jordan's King Hussein, was accorded a warm reception and a separate meeting with Soviet Foreign Minister Andrei Gromyko. He was the first Saudi official to come here since 1932, when his father, prince and later king Faisal, paid an official visit to Moscow.

Fahd's message also followed a decision by the Organization of Petroleum Exporting Countries--of which Saudi Arabia is a leading member--to establish "links" with Moscow in an effort to stabilize the world oil markets.

The Soviet Union, which is the world's largest oil producer, has been selling its crude in the Rotterdam spot market at prices below the OPEC price of $28 per barrel, thus undercutting competitors in a falling market. Moscow, which has seen its hard-currency earnings declining, has been scrambling to increase its share of western oil markets with increased supplies and lower prices.

According to poliitical observers here, the fact that Fahd had approached the Soviets suggests a significant change in the Saudi attitude toward Moscow. The Kremlin repeatedly has hinted that it wants to establish relations with Saudi Arabia, but the staunchly conservative kingdom has refused formal relations with all communist states.

There was speculation here at the time OPEC approached the Soviets in April that Moscow was now in a better position to achieve some political gains in the Middle East, particularly by reaching out toward moderate and conservative Arab states.

Apparently as part of this strategy, Moscow last month sent as its ambassador to Kuwait one of the ranking Soviet Arabists, Boghos Akubov, who had served for four years as the deputy chief of the Middle East department of the Foreign Ministry. Akubov, a trained economist, has had long diplomatic experience in the Arab world. Arab diplomats believe his mission in Kuwait is to establish contacts with the Saudis and follow financial and oil developments in the Persian Gulf.

Another indication of Moscow's courting of the Saudis was revealed by Soviet journalists who reported privately that they have been cautioned against writing anything critical of Saudi Arabia.

While the substance of Fahd's message was not known, diplomats here speculated that the interests of Moscow and Saudi Arabia may be running in "the same general direction" with respect to the Iranian-Iraqi war and sagging oil prices.

The Saudis are said to be particularly concerned about the influence of Iran's religious leaders in the Moslem world.