While an administration task force struggles to find consensus on the sensitive issue of Japanese auto imports, the White House believes that "informal approaches" to the Japanese will resolve the problem without any formal agreements.

Administration sources said yesterday that these approaches on behalf of what President Reagan calls "voluntary restraints" have received "a very positive response" from Japanese government officials.

The administration gave a veiled signal of its expectations yesterday when White House Press Secretary James Brady praised a statement by Japanese Minister of International Trade Rokusuke Tanaka saying that Japan would use "administrative guidance" to persuade automakers to stem the flow to the United States.

"That's certainly moving in the right direction," Brady said.

But neither Brady nor any other administration official would pubicly explain the basis for their optimism or define the approaches that have been made to the Japanese.

Technically, Tanaka was merely restating what has been official Japanese policy. But the timing of the statement was viewed at the White House as signaling publicly what already has been communicated privately -- Japanese willingness to head off protectionist legislation in Congress by voluntarily limiting auto exports, which reached 1.9 million cars in 1980.

Reagan believes that the Japanese government can be persuaded to impose what the president calls "voluntary restraints." He said this in the election campaign last year and again last Saturday in a meeting with the editorial board of the New York Daily News. And he will have the opportunity to make the case directly to the Japanese in a half-hour meeting Friday in the Oval Office with former prime minister Takeo Fukuda and again next Tuesday in a similar session with Foreign Minister Masayoshi Ito.

Today, the president will hear from his auto import task force headed by Secretary of Transportation Drew Lewis, perhaps the most ardent advocate within the administration of the view that something must be done to protect the U.S. auto industry. The dominant view in the task force is toward voluntary restraints, in effect a modest tilt toward protectionismin an administration where the president and his top aides are basically free-traders.

But there is not full agreement. Office of Management and Budget Director David Stockman and Council of Economic Advisers Chariman Murray Weidenbaum have warned of what they consider the dangerous precedents of protectionism, and Reagan will hear a full range of views and a briefing document with options when the task force meets with him at 11 a.m. today.

Within the inner councils of the administration, there had been concern that Reagan would be pushed into a "no-win position" in which he would have the unhappy choice of abandoning either his free-trade principles or his campaign promises to help the hard-pressed auto industry and unemployed workers.

Now, if the approaches to the Japanese succeed, Reagan could have the best of both worlds by pursuing a policy of unannounced restraints while still formally opposing import quotas.

Historically, American presidents, since the Depression have espoused "free trade" but opted for protectionism in specific cases where a powerful industry claims that it is being driven to the wall by foreign competition. While the circumstances and precise solutions differed, there were oil import quotas under Eisenhower, limitations on textiles under Nixon and restrictions on steel imports under Carter.

Reagan, however, is trying to protect the auto industry without a formal agreement, a politically attractive alternative which contains at least two dangers.

The first danger is that the Japanese will make favorable sounds that will not be followed up with real restrictions. This happened during the Nixon administration, when the president interpreted a response the Japanese thought was non-committal as indication that Japan would seriously restrict its textile exports.

The other problem is that the administration still lacks any internal agreement on what the "magic number" should be of Japanese cars. The auto industry wants a limit of 1.2 million, a reduction of about one-third. The figures kicked about within the administration have been considerably higher that that, from 1.5 to 1.7 million.

There is also the danger that the Japanese will make an agreement, either privately or publicly, and then gradually allow the level of exports to increase, as they have with other products.

But even if this happens, the view at the White House is that it would buy some time for the domestic auto industry. In the process, it would also buy time for Reagan, who at the moment, at least, is demonstrating political skill in balancing his domestic campaign promises against the imperatives of reasonably free international trade.