President Reagan, in an apparent bid to ease growing domestic and foreign concern about the danger of nuclear war, is expected to announce at a news conference this week that he endorses U.S.-Soviet negotiations to gradually reduce nuclear weapons.

Administration officials, who yesterday disclosed the president's impending move, said privately that a main aim is to prevent Soviet President Leonid I. Brezhnev from scoring a possible propaganda coup through his March 17 announcement of a moratorium on deployment of medium-range missiles in the European part of the Soviet Union.

In addition, the officials said, Reagan is anxious to counter the growing impression, underscored by recent opinion polls and a rise in domestic political activism, that his emphasis on closing what he regards as a dangerous gap between Soviet and American nuclear strength has made him insensitive to the dangers of atomic war.

In his statement this week, the officials indicated, Reagan probably will follow the outlines of a bipartisan resolution introduced last week by eight senators, including Majority Leader Howard H. Baker Jr. (R-Tenn.) and Minority Leader Robert C. Byrd (D-W.Va.).

The resolution, originated by Sens. Henry M. Jackson (D-Wash.) and John W. Warner (R-Va.), calls for the administration to "propose to the Soviet Union a long-term, mutual and verifiable nuclear forces freeze at equal and sharply reduced levels of forces."

It was intended to deal with the growing demand here and abroad for limits on the nuclear arms race between the superpowers, while still permitting Reagan to negotiate with the Soviets from a position of relative strength. By putting its emphasis on long-term, gradual reductions, the Jackson-Warner proposal presumably would permit fixing any agreement for a freeze on nuclear weapons production and deployment at a time when Soviet superiority in certain areas of atomic warfare had been eliminated.

That makes the Jackson-Warner proposal much more agreeable to the White House than another resolution sponsored by Sens. Mark O. Hatfield (R-Ore.) and Edward M. Kennedy (D-Mass.) and supported by 20 senators and and 154 House members. It calls for an immediate worldwide freeze followed by major reductions on both sides.

The administration, which says it wants meaningful reductions, has rejected the Kennedy-Hatfield plan, arguing that it would put the United States at a dangerous disadvantage because it would block plans to deploy new-generation, medium-range U.S. Pershing missiles in West European countries, halt Reagan's program of modernizing the strategic weapons arsenal and end the incentives for the Soviets to bargain on the basis of the plan put forward by the president last Nov. 18.

That plan calls for eliminating Soviet SS20 missiles being deployed in Eastern Europe in exchange for canceling the North Atlantic Treaty Organization's scheduled placement of the Pershings in West European land bases, where they would be capable of striking the Soviet Union.

The Brezhnev announcement marked Moscow's latest bid to force NATO into canceling the Pershing deployment. He coupled his call for reciprocity from the West with a warning that the Soviets might take retaliatory steps against the United States if NATO proceeds. Reagan has belittled the Brezhnev plan as "not good enough," and administration officials continue to insist that the only way to force the Soviets into meaningful nuclear arms talks is by maintaining a determinedly tough stance.

Secretary of State Alexander M. Haig Jr., interviewed yesterday on the television program "Meet the Press" (NBC, WRC), again dismissed the Brezhnev plan as a call for the United States "to quit while you're behind." Haig also said Reagan plans to make his new proposal as an announcement at the outset of a news conference planned sometime this week.