Secretary of State Alexander M. Haig Jr. expects to meet Soviet Foreign Minister Andrei Gromyko in New York next month in an effort to launch U.S.-Soviet talks on strategic arms reductions, West German sources said here today.

U.S. officials, accompanying Haig at the NATO foreign ministers' meeting here, acknowledged that Haig-Gromyko discussions were "a possibility" if the Soviet official comes to the United Nations disarmament conference scheduled for June. But the officials cautioned that no definite plans for a meeting have been made yet.

However, West German sources said Haig told Bonn's foreign minister, Hans-Dietrich Genscher, that he expects to see Gromyko at the disarmament session and intends to press for an early beginning to the so-called START talks proposed by President Reagan to cut back the intercontinental missile arsenals of the two superpowers.

U.S. officials also said there is a general feeling among the 15 members of NATO that the Soviets are prepared to begin negotiations. They added that Soviet President Leonid Brezhnev is expected to signal this willingness sometime this month in a speech replying to the proposals made by Reagan at Eureka College in Illinois on May 9.

Some sources here speculated that Brezhnev could choose as his forum a speech he may deliver Tuesday at a meeting of the Young Communist League in Moscow. In any case, these sources said, there is growing optimism within NATO that Washington and Moscow, after almost three years of delay, are again moving back on track toward a nuclear arms control accord.

The strong interest in U.S.-Soviet progress toward talks was evident even at a time when one alliance member, Britain, is on the verge of war over the Falklands, and there is deep concern about the potential effects on world peace and the possibility of the British-Argentine confrontation causing serious rifts within the alliance.

Britain and eight other NATO countries, together with neutral Ireland, are members of the European Community, which had imposed collective economic sanctions against Argentina.

However, Italy, which has strong ties to Argentina, came close to vetoing a renewal of the sanctions tonight before going along with an agreement that will effectively maintain the curbs for one more week. The foreign ministers of the European Community will meet again next week to reconsider the sanctions.

However, while discussion of the Falklands crisis reportedly played a big part in the discussions behind closed doors here today, sources in the various delegations said it was erroneous to assume that the dispute in the South Atlantic had dominated the meeting.

Instead, these sources said, the ministers had spent most of the day discussing a broad range of problems confronting the West, from Poland to the Iranian-Iraqi war, and had put perhaps their greatest emphasis on how to deal with East-West tensions.

By putting its emphasis in the East-West arena on arms-reduction talks, NATO appears to be moving away from a confrontational approach and at least partly back in the direction of detente.

That seemed to indicate a shift away from the hard line being advocated by the Reagan administration only a short time ago. Instead, the alliance now appears headed more in the direction espoused by such members as West Germany, which had been uncomfortable with the idea of a showdown over Poland and which has argued for continuing to seek areas of accommodation with Moscow.

U.S. officials are reluctant to characterize current policy as a softening of the administration's stance. But, in his presentation to the meeting today, Haig is known to have put his main emphasis on stressing that Reagan is ready to negotiate with the Soviets in good faith and is anxious to hear Brezhnev's counterproposals to his Illinois speech so talks can begin as soon as possible.

According to the sources, Haig also emphasized U.S. willingness to have negotiations that would be equitable to both sides and that would take into account Soviet concerns about including cruise missiles and long-range bombers in any reductions.