The five-year-old pact with the Soviet Union limiting offensive nuclear armaments will expire a month from today with no attempt being made to extend it formally, a senior administration official said yesterday.

At the same time, "it is quite clear that both sides want to continue discussion" of more ambitious future pacts, reporters were told. The chances for successor agreements to curb the superpower arms race were said to rest in part on Soviet willingness to abide by currently agreed restraints even after they expire on Oct. 3.

Soviet Foreign Minister Andrei A. Gromyko's meetings here Sept. 22-23 with President Carter, Secretary of States Cyrus R. Vance and other officials are not expected to produce an 11th-hour breakthrough that could stave off the lapse of the present SALT I accord, which was hailed in the Nixon and Ford administrations as a historic step toward assuring a peaceful future.

Any attempt to extend SALT I by Washington-Moscow agreement would run into a congressional demand for a full-scale review culminating in a vote on whether to approve. The administration has decided not to seek an extension, in order to avoid a potentially bruising debate in the midst of negotiations on successor pacts - and in the midst of such other controversies as the Panama Canal treaty.

A senior official, who cannot be identified under the terms of a briefing for reporters did not exclude the possibility that the United States and Soviet Union may make public statements by Oct. 3 of their willingness to abide by the current restrictions on strategic nuclear weapons after expiration. But he did not explicitly say that the Russians have agreed to this.

Congressional leaders will "very shortly" be consulted about the continuing discussions with the Russians on strategic arms, according to the officials.

Emphasizing the need to continue to abide by the current ceiling on nuclear-armed missiles and bombers, the officials said that any Soviet move to "exploit" the expiration by building up its strategic forces would have "an immediate impact" in Washington.

"It is important for the United States and the Soviet Union not to create a situation following the lapse of the agreement that one side or the other seems to be exploiting it for its own strategic ends thereby precipitating counteraction, reaction, criticisms, all of condemnations all of which have adynamic effect," the official said.

The Soviet Union is much closer than the United States to the complex limitations on missile launchers and heavy bombers set in 1972. The official said it would be possible for Russian to exceed this limit "fairly soon," for example by introducing new nuclear-armed submarines, if it decided to do so.

Soviet officials, who have recently been discussing the strategic arms question with U.S. officials here and in Moscow, have indicated "their understanding" of the issue of continuing restraint and "their concern that the negotiations continue in a positive atmosphere," reporters were told.

The central issue between the two sides on successor arms limitation pacts are the U.S. cruise missile, particularly the air-launched version which is similar to an unmanned jet plane, and the Soviet land-based missiles with independently targeted multiple warheads. The U.S. official conceded that it would take decisions by the political leadership of the two nations to achieve a breakthrough on the crucial questions.

Reporters were told that the Carter administration is adhering "strongly" to its demand that air-launched cruise missiles with a range up to 2,500 kilometers be permitted. The Russians are said to be willing to "live with" air-launched cruise missiles of that range, but only if they are counted against a sublimit of independently targetable weapons. "We will not accept" this, the U.S. official said.

The U.S. insistence on deploying long-range air-launched cruise missiles was stiffened by President Carter's decision to scrap the B-1 bomber, the official conceded. Without the B-1 as a deep penetration bomber, "we have to have the air-launched cruise missile" to insure that B-52s can continue to penetrate Soviet defenses, he said.