United Auto Workers President Douglas Fraser said yesterday that he believes the Reagan administration is privately pressing Japan to restrain auto exports voluntarily while publicly maintaining a hands-off position.

"I think in very short order we're going to find out the results," Fraser told reporters after addressing an international trade forum sponsored by the Chamber of Commerce.

The administration "is in two postures," he added. On one hand, it is maintaining a public commitment to a free position. "I also happen to think there's some tough talk going on."

Fraser's scenario coincides with reports from Japan of continuing administration pressure to resolve the auto trade issue before Prime Minister Zenko Suzuki arrives in Washington May 7, for a scheduled meeting with President Reagan.

The Japan Economic Journal has said that Secretary of State Alexander Haig last month urged that Japan hold auto shipments to the United States at the annual average in 1978-1979, or about 1.5 million units -- more than 300,000 cars below the total for last year. The publication said Haig's message was delivered through U.S. Ambassador Mike Mansfield.

The Journal also has reported that the Japanese government is considering voluntary limits of 1.6 million cars annually, a figure that it said the Japanese automakers will find very difficult to accept because their executives don't regard Japanese exports as the key reason for the deep slump in U.S. car sales.

The administration's position was stated most recently by Vice President George Bush, who said on April 6 that "the president is not pushing for numbers" in import restriction and has "stopped short of asking the Japanese" to limit imports voluntarily.

"He is for free trade," Bush said then.

But other administration officials close to the auto issue say that warnings are being delivered about the growing support in Congress for mandatory controls if Japan doesn't act voluntarily. Although President Reagan doesn't support that legislation, he reportedly has told Japanese officials he would have a hard time vetoing if it reached his desk.

Administration officials aren't predicting how the Japanese government and the auto companies will respond. Fraser said that continued pressue is necessary to force a decision. "They are the masters of procrastination," he commented.

On another issue, Fraser said officials of General Motors Corp. and Ford Motor Co. "are kidding themselves" if they believe the auto workers will agree readily to the kind of wage concessions granted to Chrysler Corp. in January. "Ford just granted a dividend and they're asking for concessions?" Fraser said. "Our members have to vote on every agreement . . . They have to be convinced there's equality of sacrifice."

Fraser also said he thought it was a mistake for Ford to reject possible joint ventures with Chrysler out of hand, as it did last week.