Washington — President Reagan's upcoming trip to Japan and South Korea is expected to yield diplomatic and political dividends. On the foreign policy front, the President hopes to foster stability in Asia by sounding the basic theme of ''Pacific partnership,'' say White House officials. He will stress peace through strength. He will also emphasize the shared values of the United States, Japan, and South Korea in fostering the free-enterprise system and democratic institutions.
Politically, the President's first trip to Asia - which is scheduled to take place Nov. 8-14 - will give him an opportunity to command the stage and to project his image as a leader of the free world and a man of peace. A visit with American troops near the demilitarized zone separating North and South Korea, say political observers, will not only buck up the troops. It will also play well to millions of veterans and other Americans back home.
Mr. Reagan travels to Japan at a time when Japanese Prime Minister Yasuhiro Nakasone himself will be seeking some domestic benefit from the visit. Mr. Nakasone is fighting for his political life in the wake of the conviction of his mentor, former Prime Minister Kakuei Tanaka, on bribery charges. With Mr. Tanaka refusing to resign his seat in the Diet (parliament), Nakasone may be forced to call an election by the end of the year. Against this backdrop, the Reagan visit could help enhance the prime minister's position as a leader and statesman.
Because of Nakasone's difficulties, US economists who are concerned about Japanese trade policy suggest that the President now has an opportunity to persuade Japan to restrict its exports to the US and open its market to more manufactured goods from the industrialized nations.
''The Japanese are anxious to have a good visit,'' comments economist Lawrence Krause of the Brookings Institution, ''so the US has leverage now.''
The admininistration is unlikely to make a frontal issue of this during a presidential visit, which is not a negotiating trip. Nakasone is in fact regarded as one of the best and most pro-Western Japanese prime ministers in recent times, and, in the view of diplomatic observers, the President would wish to do everything to help bolster his position.
Since July, however, the two sides have been holding constant meetings to try to make progress on trade problems before the trip, so that Reagan does not have to deal in Tokyo with ''citrus and beef.'' Instead, say administration officials , he will be able to focus on the broad US-Japanese relationship, stressing the importance of security, economic, and cultural ties, and calling on Japan to play a larger international political role.
''Reagan goes at a time when a country and a prime minister are looking for a new role,'' comments one official. ''The US wants to encourage it to be a close international partner.'' The President, it is added, will stress the positive aspects of trade with Japan, which is America's largest trading partner.
It is not denied, however, that with many American industries suffering as a result of cheaper Japanese imports, the administration is able to make the case in the pre-trip meetings that, if Japan is not more forthcoming in its trade policies, the US domestic political climate could turn against Japan. So both sides have a political stake in reaching early agreements.
Defense also looms high on the US-Japanese agenda. In the face of a growing Soviet naval presence in Asia, Washington has for some time been pressing the Japanese to do more to protect the sea lanes that are so vital to its economy. Nakasone has committed his nation to increasing defense spending, but the US administration would like Japan to pursue its goals more promptly. Reagan is expected to prod the Japanese on this issue, but to do so quietly.
As for South Korea, the President's visit is seen largely as a hand-holding operation. Two tragedies have befallen Korea in the recent past: the Soviet downing of a Korean Air Lines 747 and the death of 17 top South Korean officials , including three Cabinet ministers, in a bomb explosion during a visit to Burma. Diplomatic experts note that in Korean terms this represents a loss of prestige for President Chun Doo Hwan, who comes under social pressure to respond in some way.
Aware of this, the administration has moved swiftly to reassure the South Koreans of US support and to caution restraint. US officials express satisfaction with President Chun's moderation since the twin disasters. They believe the President's visit, by strongly reaffirming the American commitment to South Korea's - and Asia's - security, will further reassure the South Koreans as they continue to confront a militarily formidable communist regime to the north.
Some American critics of US policy are unhappy about the Korean portion of the presidential visit. Once again, they say, an American president is about to be seen lending his approval of an authoritarian government. Diplomatic observers note, however, that in the strategic context it is virtually impossible for an American president to pay a visit to Japan without also touching base in South Korea. Presidents Johnson, Carter, and Ford all went there during their Asian swings.
In contrast to his predecessor, Reagan has played down the issue of human rights, preferring to deal with the subject unobtrusively. Where South Korea is concerned, it is acknowledged in the administration that there are many repressive aspects of society, including a restricted press.
But it is felt that President Chun is making gradual if slow progress - by the partial lifting of the ban on political activities, for instance. It is possible that the South Korean leader will make some further moves on human rights before the Reagan visit in order to defuse the issue and smooth the presidential visit.
White House officials say the President will diplomatically mention to the South Koreans that democratic reforms are fundamental to political stability.