The United States and Japan have edged somewhat closer together in their dispute over what steps Tokyo should take to reduce its burgeoning trade surplus, and may reach agreement later this month on a compromise accord.

Sources here said yesterday there has been enough "movement" by the Japanese in the past few weeks that Robert S. Strauss, the President's special trade representative, has decided definitely to go to Tokyo for a second rould of negotiations.

If Strauss succeeds, sources say the compromise could be wrapped up by late January, Strauss' trip tentatively is scheduled for Jan. 12 and 13, following President Carter's return from his 'round-the-world trade and diplomatic tour, althought it could come sooner.

The decision for Strauss to make the trip appeared to signal some further progress in the recent U.S. effort to prod the Japanese into liberalizing their trade policies. Japan now is running an estimated $15 Billion trade surplus - almost half of it with the U.S.

Partly in response to U.S. pressure, Prime Minister Takeo Fukuda has proposed an expansionary budget for fiscal 1978 designed to bolster the domestic economy and step up Japanese purchases of foreign-made goods. And Tokyo has announced some modest tariff reductions.

After a week of bilateral talks here last month, U.S. and Japanese negotiators indicated they still were quite far apart over how much Japan should do to reduce its trade and balance of payments surpluses. American officials dismissed Tokyo's proposals as "inadequate."

However, officials said yesterday that Japan has made some further concessions in recent weeks that apparently have convinced U.S. authorities the Fukuda government is serious about its commitment to reduce Japan's trade and current account surpluses.

Along with the new stimulus package, which has proposed after the December talks here had ended, U.S. officials cited later Japanese measures to step up financing to encourgae imports and to boost Tokyo's aid to developing nations.

American sources say there also is the possibility that Tokyo may liberalize further its restrictions on imports of U.S. beef and citrus products - two key items on the Carter administration's shopping list. The Japanese had announced small tariff cuts in December.

The U.S. wants Japan to move ultimately toward flatly eliminating Tokyo's $8 to $10 billion current account surplus - a measure that includes both trade and capital flows. Tokyo, however, is resisting anything beyong a partial reduction, and the U.S. has softened its stand on that issue.

The reported new "movement" on the part of the Japanese was regarded as relatively modest, but importnat from a symbolic standpoint. Officials here concede the major element in the Japanese package is the stimulus program. The rest is important mainly to specific exporters.

However, officials here expect Japan to take additional steps later on to help pare its current account surplus further. Most observers believe the two nations will announce their accord essentially on what has been agreed on already, and leave further bargaining for later.

Strauss was not available for comment yesterday. The trade negotiator is scheduled to leave this morning to join Carter in Brussels and Paris for a series of meetings with European officials. The Paris conference will include a session with French President Valery Giscard D'Estaing.

The world's major trading nations are slated to begin serious bargaining later this month in an effort to revamp international trade rules and, hopefully, to lower trade barriers in a wide variety of categories. Officials have been pressing to complete the talks with Japan before then.