The already complicated search for a way to limit Soviet intermediate-range missiles may become even more complex because of potentially conflicting interests of U.S. allies in western Europe and Asia.

The problem, senior officials say, is that any agreement worked out with Moscow to reduce the missile threat to western Europe should not leave Japan and China more vulnerable to these 3,000-mile-range weapons.

Officials at the White House and State Department say that sensitivity to this situation has heightened here since Secretary of State George P. Shultz returned last week from a 12-day trip to Asia.

During that trip, Japanese and Chinese officials expressed concern to Shultz about Soviet SS20 missiles already targeted on their countries, about the prospect that this force might increase, and about American strategy in arms control talks with Moscow dealing with these missiles.

The complication is that those talks, and the vast amount of public attention that has been devoted to them, have focused heavily on eliminating or reducing the major portion of the SS20 force that is based in the European regions of the Soviet Union and targeted on western Europe.

Now that U.S. allies in Asia have made clear that they do not want any deal that gives Europe preferential treatment and leaves Asia as vulnerable or possibly more exposed to the Soviet threat, American officials say those differences will have to be reconciled if an agreement is to be worked out.

At the moment, there is no problem, at least officially. That is because President Reagan's "zero-zero" proposal at the Geneva talks, which began in November, 1981, calls for a "global" ban on all such intermediate-range, nuclear-tipped missiles.

It calls for the Soviets to dismantle all 600 of their missiles--about 340 of the new SS20s and 260 older SS4s and SS5s. The West, in return, would cancel deployment of 572 new American missiles scheduled to begin arriving in Europe in December unless an arms control agreement is reached.

The SS20s are the key threat because the missiles are mobile and each contains three atomic bombs in its nose. About 250 of the SS20s are based in the European portions of the Soviet Union, and about 90 in the Asian portions.

The Soviets, however, have rejected the Reagan plan. So if there is to be an agreement, it will have to be a compromise and that is where the potentially conflicting interests of European and Asian allies arise.

For example, last July U.S. and Soviet negotiators in Geneva developed an "exploratory package" of ideas that reflected a possible compromise. Although those ideas were eventually rejected, they included the possibility of Moscow reducing its missiles in Europe and freezing the number aimed at Asia.

More recently, Soviet leader Yuri V. Andropov has talked of other reduction plans in Europe but has also suggested that missiles might be moved eastward, toward Asia, rather than dismantled. This could increase the threat to Asia.

West European leaders favor working out a compromise that might at least be portrayed as a step toward Reagan's call for a total ban. But with heightened Asian determination not to be shortchanged in such a deal, it would be even more difficult to figure out where to put any SS20s that Moscow is allowed to retain.

Administration officials say the Japanese and the Chinese always were in favor of the zero-zero plan, but the degree to which they stressed it during Shultz's visit--publicly in the case of Japanese leaders--was surprising. It showed, U.S. specialists said, that the Asians were not just routinely backing a position but that they had thought hard about the issue and decided to be very specific about their views.

Shultz reportedly assured Japanese leaders that the United States would not make a deal involving European security at the expense of Asia.