The United States is showing "cautious interest" in a suggestion made last week by Soviet leader Mikhail Gorbachev for a nonproliferation agreement on chemical weapons, according to U.S. officials here and in Washington.

Such an initiative might be the type of proposal that Gorbachev and President Reagan could agree on at their summit meeting here Nov. 19-20, officials said.

In a speech in Paris, Gorbachev put forward the "thought" that "if it was possible to reach agreement on the nonproliferation of nuclear arms, why not apply the same method in respect to chemical weapons?"

He said the Soviet Union is prepared to help draft such an accord and added that it would be part of the present U.N. disarmament committee's broader effort to establish an international convention prohibiting such weapons.

A U.S. official said that there had been discussions about chemical weapons with Soviet Foreign Minister Eduard Shevardnadze during his recent U.S. visit but that nothing specific was proposed. Washington was "not looking" for such a proposal, an official said here yesterday, and was surprised by the suggestion when it was made.

Now, however, it is being considered "as an interim method to slow the spread of chemical weapons while we are looking for a ban," the official said. He pointed out that Kenneth L. Adelman, director of the Arms Control and Disarmament Agency, and Secretary of State George P. Shultz had spoken publicly earlier this year on the need to find a means to control the spread of chemical weapons.

One top Pentagon official cautioned, however, that the Soviets may be pushing the proposal "to cover over their past use of toxic weapons in Afghanistan and Southeast Asia."

Western diplomats here believe Gorbachev may have floated the idea in hopes of developing a favorable summit issue.

Faced with problems in reaching a broader agreement, "the superpowers may pick up [Gorbachev's proposal] as a fallback position," one Western European diplomat said today.

Another added that U.S. and Soviet representatives had worked together in preparing for the recently concluded nuclear nonproliferation review conference, and both nations emerged satisfied with the result.

"At no stage did they work against each other," this diplomat said.

Individuals involved in the chemical weapons negotiations here said Gorbachev may have sensed that many U.S. allies want to do something about the problem without waiting for what they expect may be years of drawn-out deliberations for a total ban on the poisons, destruction of stockpiles and verification procedures to prevent cheating.

"Gorbachev had good political sense," one diplomat said of the Soviet leader's suggestion. "He has defined an issue where it's possible for [the United States and the Soviet Union] to have a positive relationship with each other."

Another diplomat warned, however, that there were potential dangers for the superpowers if they move on a chemical nonproliferation accord and appear to be turning their backs on a broader agreement.

"Nuclear is completely different from chemical," he said. "There is no way to verify even a nonproliferation portion without a major organization," because the knowledge to make such weapons is all around and the raw materials are readily available.

In addition, Third World countries have become irritated with the superpowers, who use the nonproliferation approach to treat them as "children," one diplomat said. "They will question whether the U.S. and the Soviets really want to agree on destroying the weapons they already have," he added.

In his Paris speech, Gorbachev said Moscow was "meeting our partners in the [Geneva chemical] talks halfway . . . including with respect to verification." A U.S. official here said that the Soviets were active but that he had seen no such sign of Soviet flexibility. European diplomats said Gorbachev's statement led them to believe the Soviets now will be more responsive on the issue.