The Reagan administration believes the Japanese government will indicate its willingness to negotiate a voluntary curb on auto imports to the U.S. before Prime Minister Zenko Suzuki visits Washington in May, administration sources said yesterday.

Administration sources said they expect the Japanese to seek an auto limit agreement before Suzuki arrives to avoid any political embarrassment with Reagan. The administration is likely, however, to press for more open trade in other areas, such as gaining access to Japan's agriculture markets, sources said.

President Reagan and many of his close advisers have vehemently opposed import quotas and protection of a particular industry, sources said. However, a likely scenario in the coming months is that the administration, in its program to aid the U.S. auto industry, will expect concessions from the United Auto Workers union and the industry. In addition, an administration source said, "Congress will have to do its part" before the U.S. agrees to talk with the Japanese about voluntarily restraining imports. u

Reagan's auto task force, headed by Transportation Secretary Drew Lewis, is now working on regulatory, tax and import recommendations to the president. Thus far the task force hasn't received any commitments on concessions from either labor or management and no decisions have been made by the government, sources said.

The task force won't have a final report by Monday when Sen. John C. Danforth (R-Mo.), chairman of the Senate Finance committee international trade subcommittee, will begin a new round of hearings on the auto industry's problems. But the task force will be able to give a progress report, congressional and administration sources said.

Labor will probably be asked to hold down unnecessary wages and fringe benefits and management will be requested to invest in operations in this country rather than in overseas operations, as well as to hold down car prices, dividends and profits. In return, the government will attempt to minimize regulations that add to the price of automobiles, such as passive restraints. No new tax legislation specifically to help the auto industry so far is expected, sources said.

In the past the Japanese have been able to convince their industries to follow prudent policies by manipulating funds and benefits available to them through banks and the Ministry of International Trade and Industry, the sources said. However, companies such as Toyota are so wealthy that government armtwisting has become more difficult, but not impossible, sources said.

Danforth's legislation would limit for three years the numbers of Japanese autos sold here annually from 1.9 million last year to 1.6 million units. Reps. William Brodhead (D-Mich.) and Elwood Hillis (R-Ind.) have introduced legislation limiting Japanese car sales between 1981 and 1983 to 1.2 million cars.

During 1984 imports would be limited to 1.26 million autos and in 1985 Japanese car sales would be allowed to grow 5 percent to 1.323 million.