The American automakers, still trying to convince Japan to reduce its auto exports voluntarily, will have new evidence for their case next week -- another three months of financial losses in the industry.

Auto industry analysts expect General Motors Corp. to report a modest first-quarter profit, but Chrysler Corp. and Ford Motor Co. will add to their string of quarterly losses.

GM's profit should be about $150 million, according to David Healy of the Wall Street firm Drexel Burham Lambert. He expects Chrysler to report a $250 million loss, in the same range as its performance in the final three months of 1980, and far improved from the hemorrhage it suffered in the middle of 1980, when it lost nearly $1 billion in six months.

Ford's losses should total around $450 million for the first quarter, according to Healy.

This bad news will be duly conveyed to the Japanese automakers, who continue to resist the pressure from their own Ministry of International Trade and Industry to cut back car shipments to this country. Japanese trade officials reportedly have sought agreement on a 1.7 million-car limit for 1981, between 120,000 and 200,000 cars less than the 1980 total, depending on which side is doing the counting. So far, the Japanese car company leaders have said no.

Commerce Secretary Malcolm Baldrige warned this week that the delicate discussions between the two countries might fall through, producing no agreement or merely a "token" one that would fail to head off legislated trade restrictions by Congress.

To avert that, Baldrige urged the American auto companies and the United Auto Workers union to make new statements to the Japanese, emphasizing what the American industry and its workers are doing to help themselves.

The statements were necessary, said Baldrige, to overcome the complaints of Japanese auto executives that, with a voluntary limit on car shipments here, they are being saddled with the blame for the plight of the U.S. industry and with the burden of reviving it.

The statements by the American companies and the UAW apparently didn't win over their Japanese competitors, leaving Baldrige and his trade allies within the Reagan administration stuck with the continuing problem: how to pressure Japan into an agreement without appearing to do so.

It remains to be seen whether the Japanese car companies will be impressed by the first-quarter financial results. Despite their losses, both Chrysler and Ford have been gaining sales recently at GM's expense. During the first 20 days of April, for example, Chrysler had 13 percent of the domestic car market, excluding imports, compared with 8.8 percent a year ago at this time. Ford's market share is 24.2 percent, against 22 percent last year, while GM's has declined from 64 percent to 59 percent currently.

But the smaller two companies have paid heavily for their sales improvement in rebate programs that bled their first-quarter profits. Beginning next month, Ford and Chrysler will face competition from GM's new J-car, a four passenger compact that is larger than Ford's Escort and Lynx models and Chrysler's Ommi and Horizon cars, but smaller than Chrysler's Aries and Horizon compacts.

If the financial results don't bring Japan and the United States closer together, the next step is likely to be further pushing for passage of the bill introduced in the Senate to impose strict quotas on Japanese imports. That remains the administration's ultimate weapon -- and a dangerous one to employ