The Soviet Union has expressed interest in a U.S. proposal for wide-ranging talks between Secretary of State George P. Shultz and Soviet Foreign Minister Andrei A. Gromyko on arms-control issues, perhaps leading to resumption of full-scale negotiations on limiting nuclear weapons, a senior administration official said today.

The Soviets responded to the proposal as recently as last week by asking questions through diplomatic channels about how such talks would work, the official said.

The Reagan administration will be attempting "in the days and weeks ahead to try to get agreement to open 'umbrella' talks" dealing with arms-control issues "across the board," he said.

President Reagan first suggested such talks vaguely in a speech to the U.N. General Assembly in September and later discussed them during a White House meeting with Gromyko. They could begin in a few months if the Soviets agree, according to the official, who spoke on condition that he not be identified.

Discussing other national-security topics and Reagan's agenda for a second term, the official said:

* Reagan believes that his strategic-modernization program has been successful and that he could accept slightly lower defense spending than he sought in his first term.

The administration believes that it needs 5 percent increases in defense spending after inflation, compared with the 7 percent or more in the first term. Congress has been trimming Reagan's defense-spending requests in the last two years.

* Shultz and national security affairs adviser Robert C. McFarlane plan to present Reagan soon with a broad agenda for foreign policy in his second term, and one option includes a major increase in U.S. economic and military assistance to the Third World.

* The administration intends to continue trying to build public consensus for the need to use force in dealing with terrorism, as Shultz tried to do in a New York speech before the election.

On the proposed arms-control talks, the official said that, although the Soviet leadership appears to be in a state of flux, he thinks the Soviets will decide "by the end of the year" whether to agree.

The official suggested that the Soviets might be more willing to begin such talks now that Reagan has been reelected. Asked about prospects that the Soviets will agree, the official said, "I'm right between hopeful and encouraged."

Under the current thinking, the official said, the talks would be conducted by Shultz and Gromyko, each of whom could be accompanied by "a high-level, experienced, technically qualified expert."

While rejecting the term "czar" to describe such a person, the official said it is "a very sensible idea" to have a single expert to assist Shultz in carrying out the discussions.

In an interview with The Washington Post Wednesday, Shultz did not fully endorse the idea of naming an administration arms-control expert.

The expert would not alter Shultz's responsibilities and would "function in established channels," the official said today. The job would not be created as a means to resolve internal administration differences on arms control, as some officials have suggested, the official said.

The administration believes that the so-called "umbrella" talks would produce agreements to "split off" specific areas of superpower disagreement on arms control and resume negotiations on them, the official said.

Separate negotiations on limiting intermediate-range nuclear missiles and intercontinental ballistic missiles have been stalled since the Soviets walked out last year, protesting deployment of U.S. Pershing 2 and cruise missiles in Western Europe.

The Shultz-Gromyko talks would cover those areas and also chemical weapons, space systems, confidence-building measures and conventional forces in Europe, he said.

The official said Reagan and others in the administration have concluded that the Soviets "had laid down rather rigid requirements" for returning to the two sets of talks and that a new forum allowing "conceptual exchange" would be a "useful vehicle" to get negotiations started again.

The official said the United States earlier this year developed new negotiating positions on limiting nuclear weapons and would use the "umbrella" talks to show the Soviets that U.S. positions are flexible.

"We have developed new positions in virtually every area of arms control. In short, we are flexible. But the president does not intend to make unilaterally different proposals" before negotiations begin, he said.

For example, he said, in the ballistic-missile talks, known as Strategic Arms Reduction Talks (START), the Soviets have wanted to deal with missile-launchers while the United States sought to discuss warheads. "There are ways we can integrate those two approaches," he said.

The talks would be used to emphasize this point to the Soviets and make all of the details known before further negotiations.

The official did not provide details of new administration negotiating positions. But, he said, for example, that the United States "has some ideas" about disagreement in START over tradeoffs involving land-based missiles and those carried on submarines and bombers. The initial talks would be used not to negotiate this point but to give impetus to separate negotiations, he said.

Critics have accused Reagan of being rigid and disengaged from details of arms-control policy in his first term and allowing differing factions to squabble and frustrate the process.

The official said he rejects this criticism, noting that the Soviets walked out of the missile negotiations. But he added that Reagan would "surely" spend more time shaping administration policy on arms control in a second term and said the United States must remain "agile" in handling arms-control discussions.

The official said the "expert" envisioned to work with Shultz would be a "troubleshooter" and "designated hitter," who would "help get things back on track."

Responding to a question about candidates for the position, he said that only a "handful" exist. Among those qualified, he said, are Brent Scowcroft, who was President Gerald R. Ford's national security affairs adviser, and Paul H. Nitze, U.S. negotiatior in the talks on intermediate-range forces.

In an interview with Newsweek magazine published today, Reagan said the idea of such an expert "has come out of just general discussions that we've had without ever arriving at any decision, because we don't even know if the Russians would go along.

"And that would be a way, on this kind of informal basis, of finding areas where then the negotiators could get together, whether on arms control or any other kind of contact with them," he said.

The senior official said the administration would like the talks to begin "as soon as possible."

"We'll be ready any time," he said.