The impending expiration of quotas for Japanese auto exports to the United States is cause for little celebration here. Government officials and auto company executives seem convinced that some type of control will have to continue.

News that a Reagan administration panel has recommended that the decision be left to Japan has not softened a belief here that free trade in cars, however desirable, for the time being is politically impossible.

Trade friction with the United States has been mounting in recent months. It has been spurred by a 1984 trade deficit that, according to Japanese statistics, totaled $34 billion.

With that in mind, the Japanese government is worried that rapid growth above the 1.85 million cars a year currently allowed into the United States would heighten tension and encourage protectionist members of Congress.

One auto industry executive here suggested that the recommendation, issued by the U.S. Cabinet Council on Commerce and Trade, constituted a form of "silent pressure" by putting the issue into Japan's lap.

In recent weeks, the industry's leaders, Toyota and Nissan, have discounted predictions of a violent surge. They have cited production capacity limitations and Japanese firms' limited sales network in the United States.

But they also have hinted at self-restraint. At a press conference today, Nissan President Takashi Ishihara, who also heads the Japan Automobile Manufacturers Association, said companies here recognize the importance of the U.S. market and would be "reasonable" in their sales strategies.

The current quotas were set up in 1981 to give U.S. automobile manufacturers time to recover from being battered by recession and waves of Japanese imports in the late 1970s.

Despite the limits, the Japanese have thrived. Shifting to upper-scale models to extract maximum profit from each unit allowed, they sold $20 billion in cars in the United States last year.

Profits per car have been several-fold higher than is common in the stagnating Japanese domestic market.

Ishihara's remarks reinforced a common belief here that control will continue, though probably with a less formal framework. It might be based on "administrative guidance" from the government or private efforts by the companies.

The Ministry of International Trade and Industry is now studying the full range of options, including free trade, a senior ministry official said. "A decision will be taken some time in March," he said.

The ministry is known to be toying with a system called "weather forecasting." Under it, the Japanese government would set a target for exports and then use a variety of informal pressures to make companies conform.

In theory, such a system does not constitute direct control. But one ministry official commented, "Surely this forecast is more accurate than a forecast issued by a meteorological agency."

Officials here say that one of the most important concerns is to devise an arrangement that would not run afoul of U.S. antitrust laws.

"On the one hand, there shouldn't be any surge, American congressmen say. On the other hand, antimonopoly agencies want free trade," said a Foreign Ministry official. "That's the difficulty for us."

Japanese deliberations also are complicated by conflicts within the automobile industry.

Toyota and Nissan, which together control more than half of the U. S. export allocation, are believed to be the most satisfied with the system.

However, the six smaller companies that hold the rest of the quotas are anxious to increase their sales. Several have added new capacity to their plants with the expectation of an end to quotas.

Analysts here suggest that a purely voluntary restraint system, in which each company would be asked to use its own judgment to avoid angering Washington, would fall apart as small companies rushed to expand while they had the chance.

Despite feeling that free trade is impossible, the government and major companies in recent months have been mounting a public relations offensive on the virtues of ending restraints altogether.

One Toyota publication cites the rising profits of the U.S. manufacturers and argues that "consumers pay for the loss of free competition."

A Japanese who follows the industry calls this a classic application of "honne tatamae," a Japanese concept that translates roughly as "true feelings vs. public words."