President Reagan yesterday welcomed Vice President Bush and Secretary of State George P. Shultz back from their trips to Europe and Asia, and Bush said later that Reagan has not ruled either "in or out" the possibility of an interim agreement with the Soviet Union limiting medium-range nuclear missiles in Europe.

Bush, speaking to reporters after the 90-minute Oval Office session, said he conveyed to Reagan the "innermost feelings" of European leaders he met with, but "I just don't know" what Reagan will do with the comments and suggestions.

Bush said in London Thursday that allied leaders in western Europe had shown great interest in an interim arms agreement, even though they remain solidly behind Reagan's "zero-zero" proposal. This plan would have the Soviets remove all missiles aimed at western Europe in exchange for cancellation of U.S. plans to deploy new Pershing II and cruise missles in NATO countries.

Without commenting on a possible interim agreement, the president said in a statement yesterday that he is "deeply encouraged" by the report he received from Bush. He said progress in the Geneva arms talks depends "more critically than ever" on allied unity and U.S. "determination" to deploy the new missiles in western Europe later this year "if results cannot be achieved which make this unnecessary."

Reagan said the "zero-zero" option "is a serious one that would represent a real breakthrough in arms control.

"As such, it contrasts dramatically with the Soviet proposal which would merely preserve an existing Soviet advantage that is dangerous to the West."

The Soviets have rejected Reagan's zero-zero option, but have offered to cut the number of their medium-range missiles to 162, the same as in existing French and British forces.

However, this would allow no U.S. weapons, and has been rejected by the West on grounds that it preserves a Soviet monopoly.

Reagan said yesterday that Bush had made it clear on his trip that "we are willing to explore any serious Soviet proposal" and that the president is prepared to meet Soviet leader Yuri V. Andropov "anywhere, anytime to sign an agreement" to eliminate land-based intermediate-range nuclear missiles "from the face of the earth."

In response to a question yesterday, Bush said it is "absolutely" realistic to expect an arms agreement this year with the Soviets.

Asked what would be a serious Soviet offer, Bush said, "I don't know, but I think we'd know it when we saw it . . . . And we know an unserious offer when we see that."

Asked whether he thinks the Soviets have made "unserious" offers, Bush said, "Absolutely."

Repeating his contention made in Europe that the Reagan zero-zero option is a "strong moral position," Bush said yesterday that it is a "noble objective, it's an objective that for a while the Europeans seem to have lost sight of."

He quickly added that he did not mean "the government leaders, for the alliance is very much together on this point."

The Bush trip was designed to quiet European fears that Reagan has become too inflexible toward the arms negotiations, and he said yesterday he believes his tour "dispelled. . . the feeling that we were not interested in serious negotiations."

But while there is now "a much better perception of the U.S. seriousness and willingness" to negotiate, Bush said yesterday, "that doesn't say we have no problem. There are plenty of problems."

Bush said the comments of western European leaders, presumably including the suggestions for an interim arms agreement, would now have to be "sorted out" by Reagan and Shultz.

In his statement yesterday, Reagan said Bush and Shultz "have reinforced American policy and have set the stage for added progress in the future in two areas of the world enormously important to our country and our people."

Shultz visited China, Japan and Korea, and Reagan said yesterday he agrees with the secretary's assessment that "much of the world's future is tied up with events in Asia and the Pacific."