Administration officials yesterday expressed cautious optimism that President Reagan's State of the Union call for a new round of multilateral trade negotiations will be endorsed at the Bonn economic summit in May and launched officially either late this year or early in 1986.

They acknowledged that there are strong political and economic pressures in many countries -- including the United States -- for more, rather than fewer, restrictions on trade.

"But you can never wait for a magic moment to start a trade negotiation," said an administration official, "and 1985 will be one of the quietest political years around the globe -- there are few elections coming up. So, on timing, this is an ideal year to address trade liberalization issues."

A new round of negotiations presumably will be called the "Reagan Round," although trade experts note that a case also could be made to name it after Japanese Prime Minister Yasuhiro Nakasone, who pressed hard for agreement on a new round at last year's economic summit in London.

However named, the new round will be the eighth such series of post-World War II talks since the establishment of the General Agreement on Tariffs and Trade, which was set up to liberalize and encourage the expansion of world trade.

The most important of the recent, preceding negotiations were the Kennedy Round (the 6th), which lasted from 1962 to 1967, cutting tariffs in response to the formation of the European Common Market, and the Tokyo Round, which lasted from 1973 to 1979, which dealt seriously for the first time with nontariff as well as tariff barriers.

Officials said in interviews yesterday that a Reagan Round could last well into the 1990s and that its central theme would be to make further progress in eliminating nontariff barriers, as well as to cover under GATT rules the "emerging" trade areas related to services and high-technology items. The GATT agreements now cover mostly trade in merchandise and materials.

This week's report to Congress by the Council of Economic Advisers, advocating a new trade negotiation, said the United States "should push especially hard for liberalized trade in agriculture, services, telecommunications equipment, advanced electronics, automobiles, textiles, wood products, and steel, to mention just some of the major problem areas."

But the CEA warned that to induce less-developed countries to participate in further relaxation of trade barriers, the richer countries will have to reduce their own barriers to such products as textiles, which the poorer nations can produce and sell more cheaply.

Although the president referred to the negotiations as a new "round," some of his trade experts feel that the issues are so complex that it may be more practical to have a series of separate negotiations, each focused on one or more separate issues.

A spokesman for the Office of Special Trade Representative also pointed out that before a new round gets under way, the administration must generate a domestic consensus among business, farm and labor interests, and also must seek and obtain congressional authority for the negotiations.

Trade expert Gary C. Hufbauer of the Institute for International Economics said in an interview yesterday that "a very ambitious theme" that might have wide appeal would be to aim for a "GATT free-trade area by the year 2000." In a paper to be published shortly by the National Planning Association, Hufbauer said that such a bold plan would have to be phased in over time, with a Canadian-U.S. free trade area as one possible initial building block.

The Reagan administration, with the lead role played by William Brock, the U.S. trade representative, has been laying the groundwork for a possible new round of GATT negotiations for some time. President Reagan supported the Nakasone initiative last year at the London Summit, but the European countries -- notably France -- were cool to the idea: The communique' gave it a weak endorsement with a promise that a starting date would be considered later on.

Officials said yesterday that the Europeans now are clearly warmer to the idea, and, in fact, the European Commission has publicly endorsed a new round in principle, but without a commitment to a starting date.

Further discussions of the timetable are planned for a trade ministers meeting this coming week-end in Kyoto, Japan. There, the Europeans are expected to raise the question with Brock of whether there has been sufficient advance preparation for a new round.

Hufbauer said that since the London summit, many European countries have gained confidence in their ability to compete in export markets (in part because of the sustained strength of the dollar); and that after much internal debate, the Mitterrand government -- which opposed a new round last year at London -- may be swinging around to the view that it can compete more efficiently in the services/technology areas.

But Hufbauer also warned that prospects for a successful new round were clouded by the fact that the high exchange rate of the dollar is distorting world trade and capital flows. The huge U.S. trade deficit, he points out, generates protectionist pressures, which run directly counter to the goals of a trade negotiating round.