Soviet leader Yuri V. Andropov is prepared to meet with President Reagan in an effort to improve Soviet-American relations, according to a written interview with Andropov released today by the news agency Tass.

"Our two countries could do together a good deal of what would be useful to both themselves and to other countries and peoples," Andropov said. "The most important thing" was to reach agreements at the two sets of Soviet-American nuclear arms talks in Geneva.

He voiced the hope of a compromise in Geneva by asserting that "objectively speaking there is every possibility of this because there are solutions to the questions under discussion which do not prejudice the interests of either side."

"The Soviet leadership has always believed summit-level contacts to be a very effective method of developing relations between states," Andropov was quoted by the news agency Tass as saying in response to questions from an American journalist. "We continue to be of this opinion."

He added that "good preparatory work" was needed to ensure success for such a summit, the same precondition set by his predecessor, Leonid Brezhnev, and by Reagan.

But Andropov added: "In any case, we stand for improving Soviet-American relations and for implementing mutually beneficial treaties and agreements concluded between our countries and we welcome everything that leads to this objective."

Tass said Andropov made the remarks in reply to questions put to him by Joseph Kingsbury-Smith, national editor of the Hearst newspapers.

Kingsbury-Smith, in Washington, said he had submitted four questions to the Soviet Embassy Dec. 22 and received Andropov's replies from the embassy on Wednesday. He has received responses from every Soviet leader since Joseph Stalin, Kingsbury-Smith said.

Andropov used the questions to make his first personal comments for publication outside of his official speeches. While clearly addressing the Washington audience, Andropov adopted a lively and personal approach in an apparent effort to appeal directly to the American people.

He began by "congratulating every American family on the onset of the new year of 1983 and sincerely wishing them well-being and happiness." He added that "this means, first and foremost, wishing all Americans peace--a lasting peace and prosperity based on peaceful work and fruitful cooperation with other nations."

Andropov said that "today, the Soviet people and the Americans have one common enemy--the threat of war and everything that enhances it."

He said the Soviet Union was prepared to do "everything within its power" to reduce tensions, impose controls on nuclear weapons and end the arms race. "I would like to wish that America, too, should make its contribution, worthy of such a great country," in the same direction.

The new Kremlin leader outlined the latest Soviet proposals for arms control and voiced the hope that "the United States will reciprocate this fair and constructive position with a manifestation of good will on its part." Such a move, he said, would help ensure success at the Geneva talks and make 1983 "a good year for the whole of mankind."

"We suggest that both sides stop to build" strategic weapons immediately, he said, "that is, freeze them at the present level and then reduce the existing arsenals by roughly 25 percent on each side, bringing them down to equal levels. From there progress can be made to new reductions."

He said that Moscow was prepared to remove all medium-range nuclear weapons from the European theater if the West would do the same. This, he said, "would mean absolute zero" option for both.

The other alternative, he said, restating his proposal of Dec. 21, is for the Soviet Union to reduce its number of medium-range nuclear rockets to the combined number of missiles held by France and Britain. This would be done if the United States in turn abandons the NATO decision to deploy 572 Pershing II and cruise missiles in Western Europe .

The style and tone of Andropov's remarks stood in sharp contrast to Brezhnev's pronouncements. Moreover, Andropov sounded more optimistic about the prospects for improvements in bilateral ties than previous Soviet pronouncements suggested.

Speaking about the numbers of strategic aircraft in the European theater, he said Moscow stood "for complete equality at a far lower level than today."

Diplomats here speculated that there has been some movement in the field of arms control in recent weeks. The ambassadors of the United States, West Germany and France have called on Soviet Foreign Minister Andrei Gromyko in the past few days, presumably seeking clarifications and details on the Soviet proposals. There has been no information on the substance of these discussions, however.