Washington — With the advent of a new leadership in the Kremlin, President Reagan will keep the door open to a ''constructive dialogue'' aimed at reducing tensions in US-Soviet relations. But diplomatic experts in and out of government see little prospect of an early breakthrough. They note that:
* It will take time before the political situation in Moscow stabilizes sufficiently to enable the new leader and the Politburo to make hard decisions about nuclear arms and other issues. Even after a party leader is named, a power struggle is likely to ensue before he consolidates his position.
* Given Soviet bitterness about the Reagan administration, the new Kremlin leadership will be under constraints not to appear accommodating to President Reagan unless it can point to a concrete concession from Washington.
These among other factors figured in Mr. Reagan's decision not to attend tomorrow's funeral for Yuri V. Andropov. Vice-President George Bush will represent the United States, as he did 15 months ago, after the passing of Leonid Brezhnev.
Reagan political advisers favored the President traveling to Moscow because of the potential domestic benefits of such a visit in an election year. But diplomatic advisers argued that this would not accomplish much in foreign policy terms and could, in fact, be viewed by the Soviets as simply political grandstanding. Moreover, it was felt that the crisis in the Middle East warranted the President staying in Washington. He is to meet with King Hussein of Jordan today and with Egyptian President Hosni Mubarak tomorrow.
President Reagan, however, has struck a conciliatory posture since Mr. Andropov's passing. On the weekend he said that this change has created an opportunity for the superpowers to improve ties and that he would welcome negotiations with Moscow. ''What is needed now is for both sides to sit down and find ways of solving some of the problems that divide us,'' he said in a radio speech.
Administration officials have quickly put down speculation that this signals Reagan's desire for a summit meeting. The State Department says there has been no change in the US position that a summit must be ''carefully prepared'' and held only if it can produce meaningful results. US officials stress that both sides now are cautiously trying to climb back to the state of relations which existed before the shooting down of the Korean airliner.
Getting from A to Z is difficult, however, and the administration feels itself in something of a dilemma. Serious talks are in fact going on between the two sides on a wide array of issues, except nuclear arms. The White House wants the US public to know that, for obvious political reasons.
Yet there is concern in the administration that too much publicity of such communications risks exaggerating what is actually being accomplished. That, in turn, gets in the way of achieving concrete results, because the Soviets then back off. Hence the administration effort to convey a sense of positive movement without exciting euphoria.
The last few weeks have seen a conscious effort of the superpowers to try to take the chill off their relationship. Reagan toned down his anti-Soviet rhetoric in a speech Jan. 16. A subsequent meeting between Secretary of State George P. Shultz and Soviet Foreign Minister Andrei A. Gromyko in Stockholm further laid the ground for progress in a number of relatively minor areas.
Among the issues under discussion are an improvement in ''hot line'' communications, establishment of consulates in Kiev and New York, and a fisheries allocation for the Soviets. Recently the two sides held another round of talks on delineating the boundary between the US and the Soviet Union in the Bering Strait.
One place where the Soviets could signal their flexibility, US officials say, is in the International Civil Aviation Organization, which is discussing ways to improve navigational aids in the Far East. In addition to this, they say, Moscow could cooperate in amending the Chicago Convention to outlaw the use of force against civilian airliners.
The dominant area of superpower disagreement - the nuclear arms talks - remains stalemated. But the Reagan administation is looking at new proposals for the strategic arms reductions talks (START), which in essence would recognize the assymetry of the two sides' forces. This could beckon the Soviets back to Geneva.
But the Soviets are seen here as having a public-relations problem of their own. In recent weeks they have been playing up Soviet ''fears'' in their propaganda, thereby putting the onus for the icy state of US-Soviet relations on Reagan. Talking with the US now tends to fly in the face of that policy. Yet, if the Soviets refuse to talk, this undermines the peace image they are trying to project in Western Europe.
So both sides are proceeding with caution, wanting to step back from confrontation, but without giving up their positions. Experts do not see quick progress.
''The Russians do not want to help Reagan in 1984,'' says Malcolm Toon, a former US ambassador to Moscow. ''But if they see he is a shoe-in in November, there will be change in their tactical posture. But that is three or four months off.''
''You'll have basically the same Politburo, and these men see Reagan as trying to gain the upper hand over the Soviet Union,'' says Mark Garrison, director of the Center for Foreign Policy Development at Brown University. ''It is hard for them to set off in a new direction, especially with a new leadership. They could seize the opportunity, swallow their pride, and try to be more forthcoming. But I don't think the odds of that are high.''
Comments Dimitri K. Simes, a senior associate at the Carnegie Endowment for International Peace: ''The Soviet posture will depend on the US posture. There would have to be a sufficient administration move to let them off the hook, so they can say that they are making concessions because of a change in US policy.''
Administration officials think Soviet leaders have not yet made up their minds what to do. The Soviets are suspicious of Reagan and are upset about a resurgent United States and a perception that things are going poorly for them in the world.
Experts caution against forecasting what the new Soviet leader - be he Konstantin Chernenko or someone else - will do. They note that a Soviet leader's past performance cannot be taken as a guide to his positions once he takes power. Mr. Chernenko has the reputation of a colorless, unimaginative bureaucrat. But, experts say, this does not mean he could not head a coalition to try to reduce tensions with the West.