The United Nations is holding its breath as the United States election campaign winds down. For the next three weeks the spotlight will be on the UN as President Reagan and Soviet Foreign Minister Andrei Gromyko make their opening speeches, and as Secretary of State George Shultz meets with Mr. Gromyko.
But after these and other high-level meetings, key diplomats here predict the 39th UN General Assembly will be ''uneventful, unproductive, and dull.''
The assembly is useful as a ''diplomatic fair - just as a book fair or a business fair has its usefulness,'' says a West European diplomat.
''But speeches delivered by heads of state and foreign ministers, while interesting, and indicative of prevailing moods, do not really contribute to make things move inside the various UN chambers,'' another Western ambassador says.
Traditionally, a General Assembly held during a US election campaign is considered to be fruitless since, just before election day, US diplomacy comes to a standstill, diplomats here say. Post-election personnel or policy changes also limit the State Department's ability to launch bold new moves on important issues, at least for a few weeks.
One senior diplomat from a nonaligned nation says: ''The UN can only be productive when both superpowers want to make use of it. The Reagan administration's distaste for multilateral diplomacy has led the Soviets to keep their distance from the UN as well.
''Both superpowers now mainly stress the bilateral approach. This allows them to flex their muscles more effectively. And that leaves room for UN-sponsored, middle-of-the-road, compromise solutions,'' says the diplomat.
A European representative adds: ''The global chess game between Washington and Moscow at this time allows for no neutral areas. It is me and my friends against you and yours all the way.''
''Talking, probing, hinting, baiting, yes - but concessions, no,'' is one UN official's forcast of the posturing to be expected by key players at the General Assembly.
Despite optimistic hints uttered privately by US and Western officials, no substantial progress is expected to occur on stalemated issues such as Namibia, Kampuchea, Afghanistan, disarmament, the Western Sahara, the Falklands, or North-South economic relations. The fight between Thailand and Mongolia for a seat at the Security Council may provide one of the rare lively scenes at the coming General Assembly, according to many observers.
UN Secretary-General Javier Perez de Cuellar is said to be working carefully behind the scenes to break the ice and find some way out on issues such as Cyprus, Afghanistan, and Namibia.
''But the superpowers and their friends are stonewalling,'' an Asian diplomat says. For the moment, all eyes at the UN are turned toward the White House: ''The main question these days around here is will Reagan be reelected and which way will he decide to go after his reelection? Will he be tougher or softer during his second term?'' asks one Nordic representative.
Few people believe that President Reagan and Foreign Minister Gromyko will meet each other next week holding olive branches.
Rather, ''they may well warn each other on possible moves and countermoves they are contemplating in the global game, so as to avoid miscalculations,'' suggests a well-informed European ambassador.