PALM SPRINGS, CALIF., JAN. 2 -- President Reagan plans to be a global traveling salesman in the first six months of 1988 as he makes the case to hemispheric and western European allies for U.S. policies on arms control, the economy and Central America, administration officials said today.

A senior official who outlined the president's plans for the first half of 1988 on condition he not be identified said there is "a live possibility" that Reagan will fly to Europe this spring six weeks before his Moscow summit with Soviet leader Mikhail Gorbachev.

The European trip would focus on NATO military issues, with Reagan trying to allay allied concerns that the new U.S.-Soviet treaty eliminating medium-range and shorter-range nuclear missiles will diminish the U.S. commitment to defending Western Europe.

The dates for the Moscow summit have not been set, but the official said that U.S. and Soviet planners expect it to be held during the last two weeks of May or the first week of June.

In the week of Feb. 14-20, the president plans to meet in Cancun with Mexican President Miguel de la Madrid. The agenda is likely to include Mexico's international debt and other pressing economic issues as well as a discussion of the Central American peace process.

Two weeks after he returns from Moscow, the president will leave for Toronto to attend the economic summit of the seven industrialized democracies.

At home, officials said, Reagan will seek to avoid confrontations with Congress on most issues and seek a bipartisan consensus on arms control and other issues. They acknowledged, however, that he faces a bitter and difficult battle in his efforts to keep military aid flowing to the Nicaraguan contras.

A compromise budget package approved by Congress late last month continued nonlethal aid to the Nicaraguan rebels but required Reagan to submit any further military aid requests for the contras Jan. 25-27.

The senior official who discussed the issue here said he expects the aid request of a yet-undetermined amount to be sent to Congress Jan. 26 and a vote taken in early February. Reagan will argue that continued military aid to the contras is necessary to prod the leftist Sandinista government into implementing a Central American peace plan agreed to last August by five regional nations, including Nicaragua.

"It is uphill," the official said of prospects for further contra aid. "We have had a helluva time getting nonlethal aid of just modest amounts. It is going to be a tough fight, and if we do not win it, the freedom fighter program is over as far as the United States is concerned."

Reagan also is expected to make the case for contra aid in his State of the Union address on Jan. 25, a message that otherwise will be devoted to a broad-gauged look at the future extending to the turn of the century, according to officials familiar with early drafts.

The president sounded a characteristic note of optimism in his weekly radio speech today, saying that "we do indeed have much to be happy about as the new year commences" because "our nation is at peace" and the economy is growing at the rate of 200,000 new jobs a month.

Despite this rosy presidential view, White House surveys show growing concern among Americans with the economy and the possibility of recession. Reagan is expected to address these concerns in his State of the Union message by signaling a willingness to work with Congress on further measures to reduce the federal budget deficit.

A White House official said the president may propose a blue-ribbon commission on deficit reduction that would report after the November 1988 elections. "We need to do something that can rally bipartisan support on recommendations to deal with the deficit," the official said.

During much of his second term, particularly in 1987, Reagan has blamed Congress for the deficit while taking credit for the nation's prosperity. In his radio speech today the president returned to this theme, citing the "double-digit inflation" and high interest rates that prevailed when he became president.

"Our economic program changed all that and changed it so dramatically that today America has completed its 61st month of economic growth with low inflation," he said.

Reagan also used the speech to once more urge Senate ratification of the Intermediate-Range Nuclear Forces (INF) Treaty and Senate confirmation of his Supreme Court nominee, Judge Anthony M. Kennedy.

He concluded by referring to the American political process as "the marvel of much of the world" and by saying that "I have always loved election years."

Reagan's prospective travels to the Soviet Union, Western Europe and Mexico are seen by some White House strategists as a way to demonstrate political relevance as his influence wanes in the final year of his presidency.