The Soviet Union has sent a message to the United States that could establish the basis for an early meeting between Secretary of State George P. Shultz and Soviet Foreign Minister Andrei A. Gromyko for the purpose of restarting arms-control discussions, U.S. sources said yesterday.

The Soviet message, delivered to the State Department last Saturday, was described as a tangible sign of Moscow's willingness to meet on the arms question. One official said what remains is to establish the time and place for a Gromyko-Shultz meeting, which probably would be either in Moscow or a neutral capital in Western Europe.

It was unclear to what extent the Soviets explicitly accepted the U.S. formula for "umbrella talks" over six arms issues: strategic arms, intermediate-range arms, weapons in space, conventional forces in Europe, confidence-building measures and chemical weapons. One U.S. source suggested that the question is largely one of semantics, since the Soviets have made known their willingness to talk about a broad range of arms questions at a Shultz-Gromyko session.

A Shultz-Gromyko meeting is likely to be only a preliminary step toward resumption of detailed U.S.-Soviet negotiations. The two sides continue to have different priorities, with the Soviets most keenly interested in averting military activities in space and the United States mainly interested in reducing existing offensive nuclear arsenals.

Moreover, the substantive positions of Moscow and Washington remain far apart on nearly all the arms areas being mentioned for exploration. Some of the most contentious issues are under dispute between agencies and factions here.

A White House official said President Reagan discussed arms control in conversations last week with Shultz, Secretary of Defense Caspar W. Weinberger, CIA Director William J. Casey and national security affairs adviser Robert C. McFarlane, among others. The conversations are reported to have resulted in an "understanding" that Reagan and Shultz will have to devote more of their own time to the subject, which Reagan has described as his top foreign policy priority for his second term.

Another result of the discussion, sources said, is a consensus at top levels that a "special envoy" or "special coordinator" for arms control will be named to assist Shultz if across-the-board discussions with the Soviets can be arranged.

State Department spokesman John Hughes, while refusing to comment on Saturday's message or other communications in confidential channels, said, "We remain deeply interested in improving our relations with the Soviet Union and resuming an arms-control dialogue."

He noted that Shultz, in an appearance Friday night on the NBC Nightly News, said, "We're ready to sit down and engage in real negotiations with the Soviet Union on arms control and seek concrete results and work out problems." Shultz was responding to written statements from Soviet President Konstantin U. Chernenko to NBC News correspondent Marvin Kalb.

Kalb, on Monday night, was the first to report the delivery of Saturday's message from the Soviets.

A senior State Department official discouraged speculation that an early summit meeting between Reagan and Chernenko might result from a Shultz-Gromyko exchange. Chernenko, in answers to questions from Kalb, said he did not believe that the time was right for such a meeting.