President Reagan announced yesterday that he is prepared to discuss "serious proposals" with the Soviet Union on reducing nuclear arsenals and that he will send Vice President Bush to western Europe Jan. 30 to meet with allied leaders and the pope.

Bush will be traveling to eight European nations about the time the Reagan administration must decide on its negotiating position for nuclear arms talks with the Soviets, scheduled to resume in Geneva early next month.

"A cornerstone of our approach to relations with the Soviet Union is close consultation with our allies on common political and security issues," Reagan said in his Saturday radio broadcast from Camp David, Md. "In this spirit, I've asked Vice President Bush to travel to Europe."

In his broadcast, Reagan added that improved relations with the Soviet Union "must result from moderation in Soviet conduct, not just our own good intentions . . . . We and our democratic partners eagerly await any serious actions and proposals the Soviets may offer and stand ready to discuss with them serious proposals which can genuinely advance the cause of peace."

Reagan said Bush also will meet with U.S. arms negotiators in Switzerland and attend a meeting of the Committee on Disarmament in Geneva. Sources said that Bush may carry with him changes in the U.S. bargaining position at the arms talks but that the administration has not decided what proposals it will put forward at the talks.

White House officials said Bush's trip is intended to counter the widening anti-nuclear movement in western Europe and the impact on public opinion there of a recent Soviet offer to hold a summit meeting.

The Soviet offer has drawn support among European leaders eager for a summit that might help reduce tensions between the two most powerful nations. The vice president plans several speeches on arms control while in Europe, according to a spokesman.

Bush's trip would occur six weeks after Secretary of State George P. Shultz completed a similar trip through seven western European capitals.

He sought to allay European fears about use of nuclear weapons and the chances for success in parallel negotiations with the Soviets about medium-range missiles based in Europe and talks on intercontinental missiles the U.S. and the Soviet Union have aimed at each other.

Like Shultz, Bush is to travel to the five nations where the United States and its allies want to deploy new Pershing II and cruise missiles: West Germany, Britain, Italy, Belgium and the Netherlands. In addition, Bush is to visit Italy, France and Switzerland.

In his broadcast, Reagan referred to Soviet use of "negative" tactics of "trying to sow division between the American people and our NATO North Atlantic Treaty Organization partners." Reagan said such strategies could only delay progress in arms talks.

"The vice president's visit to these close friends and allies, and his discussions at the Vatican and in Geneva, underscore our fundamental commitment to peace and security in Europe and to genuine arms reductions," the president said.

A spokesman for Bush said the vice president is not scheduled to meet with Soviet officials in Geneva. But White House aides said Bush will be in position to determine informally if the Soviets have proposals substantial enough to merit a summit meeting.

Bush headed the U.S. delegation to Moscow for the funeral of Soviet president Leonid I. Brezhnev in November and, with Shultz, met and talked with new Soviet party leader Yuri V. Andropov.

Andropov's offer of a summit late last month brought little response from Reagan. A White House spokesman said last week that the proposal contained "nothing new" and, at his news conference Wednesday, Reagan said a summit has value only after it has been planned and when he can be sure that there are specific proposals to be discussed.

Last week, the Soviets proposed a nonaggression treaty between NATO and the Warsaw Pact nations, but Reagan said Wednesday that it could be considered only after consultation with the NATO allies.

"As you know, a new leader has come to power in Moscow," Reagan said yesterday. "There has been much speculation about whether this change could mean a chance to reduce tensions and solve some of the problems between us. No one hopes more than I do that the future will bring improvement in our relationship with the Soviets and an era of genuine stability." Later in the broadcast, however, Reagan noted that, when the United States made efforts to reduce its military buildup in the 1970s, the Soviet response was to "accelerate their military buildup, to foment violence in the developing world, to invade neighboring Afghanistan and to support the repression of Poland."

"The lesson is inescapable," he said. "If there are to be better mutual relations, they must result from moderation in Soviet conduct, not just our own good intentions . . . . Moderate words are convincing only when they are matched by moderate behavior. Now we must see whether they're genuinely interested in reducing existing tensions . . . ."

Reagan described specific steps that he apparently feels would indicate that the Soviets are serious about reaching accommodation on arms control. They include "ending the bloodshed in Afghanistan," allowing reforms in Poland and "showing restraint in the Middle East."

In the Democratic response to the president's remarks yesterday, party chairman Charles T. Manatt applauded Reagan's decision to send Bush to Europe and called for the president to agree to a summit.

"This is a subject that requires presidential leadership," Manatt said. "The time has come for the president of the United States to sit down with the leader of the Soviet Union, face to face, to make a determined effort . . . to halt the dangerous race to nuclear confrontation."