A U.S. proposal to nearly double the planned amount of American aid for Greece next year has brightened prospects for an agreement on the future of U.S. military bases here, according to Greek and U.S. sources.

Barring unforeseen difficulties, Greek government and opposition leaders alike now expect the swift and successful conclusion of the six-month-old talks.

The negotiators themselves, however, believe that difficult discussions still lie ahead to resolve a number of obstacles when the talks resume here April 11, according to diplomatic sources who claim to be close to the talks. This professional prudence reflects memories of previous agreements that were initialed but never ratified.

Socialist Prime Minister Andreas Papandreou only this week voiced optimism about arriving at agreement "within one or two months" on a "political framework" of a deal. This is a far cry from his opposition days, when his call to abrogate the 1953 agreement establishing the bases helped sweep his Pan Hellenic Socialist Movement to an outright parliamentary majority in the 1981 elections.

Also indicative of a more sanguine Greek approach was a statement by government spokesman Dimitris Maroudas that for the first time dwelled on progress in the talks.

In fact, the fourth round of talks conducted by Yannis Kapsis, undersecretary of state for foreign affairs, and special U.S. envoy Reginald Bartholomew started last month in a far less serene atmosphere.

Suspended for eight days at one point, the talks were surrounded by Greek suggestions of deadlock and took place against a background of a leaked American aide-memoire critical of Greek government action surrounding the visit of Soviet Premier Nikolai Tikhonov.

But when the talks resumed, the United States had agreed to raise the amount of annual mutual assistance proffered Greece from $280 million to $500 million for fiscal year 1984. Congress must approve the level of aid.

Aid at the proposed figure would reestablish approximately the 7-to-10 ratio that over much of the past decade has set a pattern whereby Greece received 70 percent as much assistance as its larger and more populated neighbor and rival, Turkey.

Greek perceptions of a pro-Turkish tilt by the United States during the Turkish invasion of Cyprus in 1974 set off demands in Athens under first conservative and now Socialist administrations for a new deal on the American bases.

One deal was initialed in 1976 but never ratified by Greece, whose government then believed a better arrangement could be found.

Symptomatic of the recently improved atmosphere was the assurance of a high Socialist party official close to the prime minister who said the government was happily surprised to find an understanding administration in Washington.

In a country where anti-Americanism remains deep seated--in large part because of U.S. support for the military junta that seized power here in 1967 and fell because of its inability to stop the invasion of Cyprus--such a volunteered compliment represented something of a new departure.

The official gave U.S. Ambassador Monteagle Stearns--who has served two previous tours here in more junior positions--much of the credit for improving relations between Athens and Washington.

No known American diplomatic demarche has complained about a series of demonstrations organized by Papandreou's Socialist party and the pro-Moscow Communist Party in Athens, Patras and other cities protesting the continued presence of the U.S. bases.

Following Tikhonov's visit in late February, the aide-memoire from Richard Burt, the assistant secretary of state for European affairs, was leaked, apparently by leftist elements within the Greek government. It did not deal specifically with the bases. Rather it reproached the Greek government for approving a recent Warsaw Pact proposal for a nonaggression treaty and establishing a nuclear-free zone, policy decisions described as "still another step" on Greece's "departure from allied unanimity" inside NATO, according to the Greek version published by a satirical weekly here.

A State Department source in Washington said the department would not comment on "diplomatic communications."

Earlier, the U.S. administration was known to have been upset by Papandreou's odd-man-out dissent within NATO on everything from how to deal with Poland to the European peace movement.

The Papandreou government did nothing to play up the leaked American aide-memoire as unacceptable interference in Greece's foreign policy, which Papandreou has styled "multidimensional."

By that Papandreou has meant that Greece should no longer automatically aid western, especially American positions, as previous governments have done since World War II.

Although the outstanding remaining issues in the negotiations have not been identified, Papandreou has said that any future deal on the bases must satisfy Greek demands for a timetable for their eventual withdrawal--thought to be no more than 10 years--arrangements for sharing information, and satisfaction on the money available to improve Greece's armed forces.

Some cynical Greeks are convinced that the government has little interest in concluding a deal if only because it will fall short of Papandreou's previous demand for a quick and total end to American military presence on Greek soil.

Some observers have suggested that Papandreou may try to sell any agreement on a framework deal as a political victory but then allow the details on any accord to get bogged down in technical talks.

Although even before his 1981 election victory Papandreou had watered down his demands on closing the bases, some political observers expect he may face trouble from the Communists and the extreme left of his own party if and when a deal is struck with the United States.

However, even the most disillusioned leftists interviewed here conceded that he will have no problem in getting Socialist deputies--who hold 175 of parliament's 300 seats--to ratify any deal he supports.