The Falkland Islands war--and its relevance to Greek-Turkish territorial disputes in the island-dotted Aegean Sea--is likely to catch up with Secretary of State Alexander M. Haig Jr. when he arrives here Saturday for talks with Greek Premier Andreas Papandreou.

Haig is the first top-ranking U.S. official to visit Greece since Papandreou and his Greek Socialist Party were elected in October on a platform of closing American bases here and pulling Greece out of the North Atlantic Treaty Organization.

Tonight 30,000 supporters of the Moscow-oriented Greek Communist Party demonstrated here to protest Haig's visit and Papandreou's failure to carry out the campaign pledges. Western observers said the protesters also included many members of Papandreou's Socialist Party who are critical of his foreign policies.

The chief purpose of Haig's talks here is to open a negotiation process to revise the operating agreement for four major U.S. bases in Greece. But it is expected here that the troubled relations between Greece and Turkey, neighboring members of NATO, will affect the discussions.

Since 1974, Turkey and Greece have disputed continental shelf and airspace rights in the Aegean Sea, where the profusion of islands and underwater projections of the mainland have created conflicting territorial claims.

U.S. refusal to formally guarantee Greece's eastern borders with Turkey is believed to have contributed to a breakdown in negotiations to revise the 1953 bases agreement last June, under the previous, conservative New Democracy administration of George Rallis.

Observers expect Papandreou to link the issue of Greek security against possible Turkish aggression to the subject of the bases.

U.S. officials here indicated that the United States would be loath to include a guarantee of Greece's eastern borders in a Greek-U.S. agreement, a move that could alienate Turkey.

Greek government sources indicated that Athens might point to the Falklands invasion as an object lesson showing the need for security guarantees for the Aegean island border with Turkey.

"Turkey has a 150-landing-craft force and an army of 120,000 men on its Aegean coast, which can only be directed against the Greek Aegean islands," one source said. "We feel that certain conclusions on the basis of the Falklands crisis are inevitable."

The same sources said, however, that Papandreou would be more flexible than the Rallis government on what he considers an acceptable guarantee.

"It need not be in the form of a verbal guarantee," one official said. "The provision of certain kinds of military hardware would be one way of making us feel safe. Or a certain psychological climate could be created in the region."

In Ankara, a senior U.S. official accompanying Haig played down reports from Athens that Papandreou will press for some kind of guarantee on Greek sovereignty in the Aegean, Washington Post staff writer John M. Goshko reported. The official contended that the subject "has been dealt with in recent weeks and has been almost completely settled." Haig "does not expect it to be very high on the agenda" of his Athens talks, the official said, but added, "Maybe we'll be surprised."

It is expected here that Papandreou's message to Haig will be that talks on the bases are likely to be much smoother if the United States uses its influence to help settle the Greek-Turkish dispute within the NATO framework. Papandreou also is likely to bring up the issue of Cyprus. He is trying to get U.S. and Western European support for a withdrawal of the Turkish troops on the island.

Despite expectations of the Communist protests, Greek and U.S. officials here painted a picture this week of an unprecedentedly positive climate of relations between Athens and Washington on the eve of Haig's arrival.

"We expect all talks to be conducted in a friendly atmosphere," one Greek government source said.

A U.S. official said, "The Greek side is definitely approaching the bases issue in a constructive spirit. We feel it is not so much a matter of 'if' an agreement on the bases is signed, but 'when'."

Greek positions on the bases and related issues were conveyed to Washington last month by U.S. Ambasador Monteagle Stearns. Talks on the bases are expected to begin in late summer or early fall. The issue also is to be discussed by Papandreou during a planned meeting with President Reagan at the NATO summit meeting in France in June.

During a visit to Algiers this week, Papandreou told the Algerian newspaper El Moujahid: "Our ultimate goal remains the removal of the bases. But we do not wish to have a conflict over this issue and will abstain from unilateral moves. We are obliged to take into account certain strategic facts and the existing world balance of power, as well as our own national interests."

U.S. officials say that the activities of at least three of the four main bases could largely be transferred to satellites in seven or eight years.

But both sides say that the Souda Bay base in Crete is a more difficult problem. The bay provides natural harbor facilities that can accommodate almost all of the U.S. Sixth Fleet.