Senior Soviet officials have indicated a willingness to consider "significant" cutbacks in nuclear weapons stockpiles in any future negotiations about strategic weapons, according to the head of a U.S. Senate delegation visiting here.

Sen. Joseph D. Biden (D-Del.) said he also detected tacit Soviet acceptance of more comprehensive verification procedures than under the SALT II agreement, an attitude that could lead eventually to onsite inspections.

Biden and five other senators have looked for possible Soviet attitudes toward prospective negotiations on a third strategic arms limitation treaty during three days of meetings with Soviet officials.

Biden added that Soviet officials, during four plenary sessions devoted almost exclusively to strategic arms matters, accepted without strong demur the senators' assertions that such powerful Soviet tactical nuclear weapons systems as the SS-20 and Backfire bomber must be specifically included in any successor to the SALT II agreement. SALT II was signed by President Carter and Soviet leader Leonid Brezhnev in June. The treaty has come under sharp criticism from some senators who are expected to vote on its ratification in early winter.

According to one delegation source, th Soviets' attitudes were suggested as much by such silences as by specific Soviet retorts to the senators' statements. Biden and Sen. Richard Lugar (R-Ind.) indicated this was notable especially in the Soviets responses to the senators' repeated assertions that the Senate will insert "modifications" or "reservations" into the pending SALT II.

The Soviets were said to have listened carefully to the senators' explanations of these proposals and reportedly made no substantive reply. This calm response by the Kemlin group, which included deputy chief of the Soviet general staff Sergei Akhromeyev, a strategic arms specialist, was in sharp contrast to the grim warnings by Brezhnev and other Politburo leaders that the Soviet Union would never accept modification of the accord, which took seven years to negotiate.

The senators met today with Soviet Premier Alexei Kosygin in what Biden and Lugar described as a "very cordial," three-hour session devoted to detailed discussion of SALT issues.

They said Kosygin engaged them in lively debate on various points, but that the session was not marred by bitter disagreement.

The U.S. delegation, which also included Sens. David Boren (D-Okla.), Bill Bradley (D-N.J.), Carl Levin (D-Mich.) and David Pryor (D-Ark.), arrived in Leningrad last week as guests of the Supreme Soviet, the figurehead national legislature. It is the sixth such delegation of senators or congressmen to come here in the past year and probably the last before the Senate moves to a final vote on the arms treaty.

Biden said Kosygin, who last year belittled the Senate in an angry flareup with a group led by Sen. Abraham Ribicoff (D-Conn.), seemed to understand both the role of the Senate and the importance of six votes on such a narrowly divided issue.

As the delegation leader, he told the Soviets during the Kremlin sessions that likely Senate treaty reservations will include:

A provision that the Senate considers the "statements and common understandings" accompanying the treaty to have the same binding force as that document itself.

Opposition to extension of the treaty past 1981.

A provision ensuring that the treaty's "noncircumvention clause" does not rule out U.S. help to NATO allies to modernize intermediate range strike forces.

A provision that the president must abrogate the treaty if the Soviets are found to have violated Brezhnev's nontreaty promises limiting the Backfire bomber.

A committee source said the Soviets generally mildly expressed the view that "these were internal matters of the United States" and thus no business of the Soviet officials.

Although the group planned to test Soviet reactions to the current Senate debate on SALT II, the discussions focused strongly on SALT III as well. Biden said the Soviets indicated willingness to negotiate tactical nuclear force strengths in Europe, that they also agreed that progress in dealing with the complex issues raised by such "forward based systems" and the cruise missile must be made well ahead of the SALT II protocol expiration.