Congress will insist on having a voice in any formal extension of the American-Soviet agreement for limiting offensive strategic nuclear weapons due to expire on Oct. 3, Capitol Hill sources said yesterday.

President Carter said in a recent interview that he sees no need for Congress to legislate on an extension. His administration is anxious to avoid opening the door to what it fears might turn into a bruining debate in the midst of sensitive negotiations with the Soviet Union.

Negotiations are due to resume in Vienna on Sept. 7 between Secretary of State Cyrus R. Vance and Soviet Foreign Minister Andrei A. Gromyko. There is no realistic expectation that the Vance-Gromyko talks could produce a complex, new nuclear agreement by the time the current five-year limitation runs out Oct. 3, although the administration officially leaves that hope open.

What the Carter administration is attempting to devise, an officail said yesterday, is "a bridging agreement" that can be worked out with the Soviet Union, and gain congressional acquiescence, without touching off a major debate.

It is the latter task, avoiding a legislative controversy, that is the most difficult problem.

The President, in a July 29 interview with Time magazine, repeated as he and Vance have stated before, that if there is no new nuclear agreement by Oct. 2, "my hope would be that we could extend the present agreement for a period of time."

He was then asked if the extension would be "in the form that would require any kind of congressional approval."

Carter replied, "No." He said, "I think there would be a general acceptance on the part of my administration and the Soviet leaders if we simply extended this present agreement. I don't think there would be any challenge to the legality of it . . ."

When asked if the extension might be "a memorandum initialed" by Vance and Gromyko, Carter replied, "Yes. That would certainly be binding on me."

The Senate Armed Services subcommittee on Arms Control, headed by Sen. Henry M. Jackson (D-Wash.), will insist that "any formal agreement" between the United States and the Soviet Union to extend the nuclear accord must be submitted to a vote in Congress, according to subcommitte staff members.

"The statute [creating the Arms Control and Disarmanent Agency] is clear," a Jackson subcommittee specialist said yesterday, "that any agreement that limits the arms of the United States requires congressional approval."

A recent study by the Congressional Research Service of the Library of Congress reached the same conclusion:

". . . It can be expected that Congress would insist that a proposed extension of the interim agreement would require 'affirmative legislation' - most likely in the form of another joint resolution."

The arms control agency's legal office agreed yesterday that "a formal agreement" on arms control requires either treaty approval by the Senate, or other legislation by the Senate and House.

In one sense, that is a more clear-cut position than the Nixon administration took when the 1972 nuclear agreements were submitted to Congress. They were the treaty of indefinite duration to limit defensive antiballistic missiles, plus the expiring five-year limitation on offensive, intercontinental missiles and bombers.

The Nixon administration was divided on whether it was legally obliged to submit the so-called interim accord to Congress, but said it wanted Senate-House approval through a joint resolution to avoid controversy and to record national approval.

What the Carter administration now seeks, however, according to officials, is congressional acquiescence to extend the five-year agreement for "a limited time," hopefully without a vote and debate, until a more permanent U.S. Soviet accord can be negotiated.

"Exactly what form this will take really hasn't been resolved within the executive branch," an official said yesterday. He said both the legal and policy questions are "under active study."

Congress "will be very actively consulted before there are discussions with the Soviet Union," and "whatever concerns Congress, will be addressed," he said.