ON A RECENT VISIT here, an East European functionalry of high professional qualifications stunned the executive of an American corporation, a man he had met during his frequent previous trips, by asking for a job. After driving a hard bargain on salary, function and title, he said he would return home to wind up his affairs. He will ask for political asylum here only on his next mission, some time later this year, and then start his new job and new life.

Why was he in such a hurry to arrange for a job here?

He wanted to beat the rush. Like other East Europeans -- as well as Western observers -- he expects an exodus this summer. The reason: continuing tension over the fate of Poland.

Specialists in refugee issues do not want to make alarming predictions.But their off-the-record feeling is that this summer's total may reach 50,000 -- the highest since the 1968 invasion of Czechoslovakia -- even if the Soviets do not make a move into Poland.

If the Red Army does march in, a mass exodus is likely -- a repeat of 1956, when 180,000 Hungarians fled to Austria and Ugoslavia before the Soviet-installed government sealed the borders, and of 1968, when 100,000 Czechoslovaks left for Western countries using passports issued under Alexander Dubcek's liberal regime.

Already the number of East Europeans awaiting resettlement in Austria, their traditional transit camp, has passed 13,000, compared to 2,350 a year ago at this time and the highest since 1968.

What makes the 1981 exodus different is that it is from all the countries of the Soviet bloc. The largest number of the refugees are Poles -- more than half -- followed by Czechoslovaks, Romanians and Hungarians.

Not only the Polish crisis is involved in the decision to emigrate. Throughout Eastern Europe, people are worried about the end of the prosperity created during the 1970s by the influx of Western capital and goods under the aegis of detente. An aggravating factor is food shortages in every country except Hungary, which has revolutionized its agriculture with American equipment, and East Germany.

The Austrian government has appealed for international assistance, and asked the United States, Canada and Australia to speed up processing immigrants. In May the number of arrivals shot up to 1,700 in Austria and another 500 in other West European countries -- about nine times as many as a year ago -- and the figure for just the first half of June exceeded May's total.

Another Soviet invasion of a neghboring country would prove its intended point throughout Eastern Europe: that resistance to Moscow is futile. But it also would suggest that communism cannot reform itself from within. The reaction would be an epidemic of gloom. In the collective humilation that follows an invasion everybody seems to want to leave the country. But of course not everyone can; only a minority with connections or courage do, leaving those who stay behind feeling even more abandoned and depressed.

A Polish diplomat here fears "a massive brain drain" in case of a Soviet invasion. "The church is the only force that can keep our people home," he said. He argued that only the Catholic church, which doesn't want to lose its parishioners, can persuade patriots to stay; the Communnist Party would be laughed at if it made the same appeal.

Many thousands of Poles now in the West on tourist visas keep extending their stay, pending a resolution of the crisis at home. In case of an invasion, they are likely to file for political asylum.

Sweden and Denmark have publicly pledged that their naval forces would protect Poles crossing the Baltic Sea. It is understood that such protection extends beyond their territorial waters to the high seas -- wherever a Pole may reach their vessels to request asylum. "We will do our utmost," a Swedish diplomat here said. He recalled that Polish naval units, including submarines, has found sanctuary in Swedish ports after the Nazi conquest in 1939 and that Sweden had given asylum to some 50,000 Baltics, mostly Estonians, after the Soviet annexation of three Baltic republics in 1941.

In the United States, the annual quota of 5,000 East European refugees will soon be filled for the 1981 fiscal year that ends Sept. 30; next year's request is under study. As in the case of last year's Cubans, the administration has to decide if this year's East Europeans qualify as political refugees. The Immigration and Naturalization Service maintains that if a person applying for immigration talks about economic reasons, he is an economic migrant and thus has to wait for his turn as an applicant on the regular immigration quota. The State Department, which has thus far won the debate, argues for political refugee status even if a person cites economic reasons but cannot return home without fear of persecution.

In a few days, a cabinet-level task force on immigration and refugee policy is expected to submit its report to President Reagan. Under the 1980 Refugee Act, the president has the authority, after consultation with Congress, to grant admission to large, "unforeseen" groups of refugees -- an emergency category beyond the ceiling, set at 217,000 refugees in fiscal 1981.

Since Eastern Europe has been under communist domination for more than three decades and the majority of the population grew up under communism, a high percentage of the refugees these days are Communist Party members, some of them second-generation Communists.

U.S. immigration law no longer raises serious obstacles for party members who seek political asylum here. In West Germany, the other magnet for East Europeans, the government strongly favors the resettlement of refugees from communism and confers citizenship not only on East Germans but on all those who can claim, however remotely, German origin. Of West Germany's population of 60 million, about 12 million are refugees of German extraction.

Sweden is particularly generous in helping refugees with jobs, apartments, medical treatment, even cars. According to United Nations statistics, Sweden leads the world in per capita contributions to refugee relief: $3.98 in 1980. The U.S. figure is 90 cents. The United States is 12th in per capita contributions, but first in absolute numbers, with $222.5 million.

Every year hundreds of Soviet bloc citizens slip across the 10-foot-tall barbed-wire fences and electronic fortifications of the frontier zones. The ones who make the news are the likes of a Czech family crashing through to West Germany with a home-made armored car or a Romanian landing a crop-duster in Austria after flying hundreds of miles at three level to evade radar. But neither is it all that easy for those lucky enough to have passports. Their spouses and children are usually kept behind as hostages, yet they cannot help thinking: Will I be given another chance to be in the West? And what if I don't return home?

These days as many as 400,000 Hungarians a year are allowed to travel to the West -- and about as many Poles. They visit relatives; go on one-week group tours of Rome or Paris; or spend a weekend in Vienna, the highlight of which is a Sunday afternoon's rooting for the national soccer team playing against Austria.

Czechoslovaks granted similar privileges number in the thousands -- the figure is lower for Romanians, and down to only a few hundred in case of Russians and Bulgarians.

The intention of a liberalized passport policy has been to ease the many tensions that the closed-in, "concentration camp feeling" produced during Stalin's days, when an East European could not even visit a neighboring communist country except on an official mission. But the net result has been that some of those traveling to the West do not use their return tickets.

Hungary, which prides itself in maintaining the most liberal passport policy, has been losing more than 10,000 of its citizens a year -- a large number for a nation of 10 million. Most of them join friends and relatives in West Germany, Austria and Sweden, where professionals such as physicians and engineers have little trouble having their university degrees promptly recognized. Some go as far as the United States, Canada and Australia.

American professionals are often amazed by the outspoken anticommunism of visiting Soviet bloc colleagues. "Oh, the regime has changed and we are allowed to say such things," is one explanation given; another stresses that the host is trusted. Many Americans have felt that their Soviet bloc guests at least faintly probe reactions to the possibility of settling here. Occasionally, an East European invites a detailed discussion of what he might do in case he decided to live in the West.

For those whose applications to visit the West are turned down, Yugoslavia offers a way out. "We don't police our borders for Warsaw Pact states," is the stiff Yugoslav response to queries about Soviet bloc citizens reaching the West through Yugoslavia. Because of Yugoslavia's special status as a communist though nonaligned country, it is much easier for a Soviet bloc citizen to obtain a passport valid for a trip to Yugoslavia than to, say, neutral Austria. From Trieste to Venice is an hour's train ride with only a cursory passport inspection. One may also walk across the border -- for a few dollars, a friendly Yugoslav farmer will serve as a guide. A watch or a camera will buy a ride to an Italian or Austrian village.

Once in the West, a Soviet-bloc citizen calls the police or the embassy of the country where he intends to seek political asylum.While his application is investigated, he is put up in one of the refugee camps in Austria, Italy or West Germany that have not stopped functioning since the end of World War II.Should he want to come to the United States, it may take several months before his case is decided. Those who receive priority are relatives of U.S. citizens and residents.

The process is not always sympathetic. Unpleasant questions about past associations are routinely asked in interviews that can extend for hours. The refugee is sometimes reminded that he should consider himself speaking under oath. It is always a surprise to learn that Americans put a premimum on the truth -- a currency long ago devalued in Eastern Europe.