The timing is bad. The margins of outside influence are slim. But both Europe and the United States think the West should now offer a new beginning in East-West relations to Soviet General Secretary Konstantin Chernenko.
Alliance harmony on this point is striking as US Vice-President George Bush, British Prime Minister Margaret Thatcher, and West German Chancellor Helmut Kohl all pay their respects at Yuri Andropov's funeral in Moscow. It contrasts sharply with internal Western strains as Mr. Andropov succeeded Leonid Brezhnev 15 months ago.
In the analysis of American and European diplomats two developments account for this welcome difference:
* NATO's success in proceeding as planned with deployment of new NATO nuclear missiles in West Europe (and Moscow's conspicuous failure to block them).
* President Reagan's election-year move away from ideological confrontation toward foreign-policy pragmatism.
A senior European diplomat in Bonn summarized the first point crisply: ''Magnanimity in victory is a good diplomatic and even a good power political principle. We should not now seek to rub Soviet faces in this Soviet failure but should offer them dialogue with both hands.''
This European attitude is hardly surprising. For some months the European maxim has been to speak softly while carrying the stick of NATO deployments to foil the Soviet try for theater nuclear superiority with the SS-20. West Germany has consistently spoken softly over the past several years. Mrs. Thatcher, who once relished bear-baiting herself, has just smiled at Moscow with her first official visit to a Soviet-bloc country, Hungary.
And French President Francois Mitterrand, despite the delicacy with which he must avoid enhancing the prestige of the French Communist Party domestically, signaled his own fresh start this month in the visit to Paris of Soviet First Deputy Prime Minister Ivan Arkhipov.
What was less certain, perhaps, was how far the Americans would play along with an approach to the Kremlin that treated the Soviets as legitimate negotiating partners rather than an ''evil empire.''
To be sure, the US signed on to the joint NATO statement last December that offered the Kremlin Western cooperation as well as confrontation. But American endorsement then seemed to be less a matter of conviction than of humoring the Europeans.
Reagan made his own conciliatory overture to the Soviets on the eve of the Stockholm conference a month ago, however, and he is talking to the new Kremlin leadership in the same tone.
This time around, it is not a question of Europeans persuading Washington to take a more conciliatory line (or the Americans suspecting that Europeans are cowards in addressing Moscow). Both sides of the Atlantic have come up with the same approach, as an American diplomat notes, ''spontaneously'' and not in any ''orchestrated'' way.
This united Western approach does not hold out hopes of restoring anything like the East-West detente of the 1970s. It does not even promise a quick return to nuclear arms control negotiations. But diplomats think it does stand a reasonable chance of getting East-West contacts out of the cold-war depths to which they have sunk.
In this context Western diplomats point out that Brezhnev's protege Chernenko fits into the mold of collective leadership established by Brezhnev. He is not going to try solo initiatives, either in new military adventures or in cozying up to the West.
Veteran Foreign Minister Andrei Gromyko will surely be embodying substantive as well as personal continuity in Soviet foreign policy. And Chernenko, who is probably the one Politburo member apart from Gromyko who feels most at home in international affairs, is unlikely to make the kind of mistakes that a neophyte like Leningrad party chief Grigory Romanov might make.
The timing is not especially propitious just now for a full ''normalization'' of East-West relations in any case. The Soviets are still smarting from the failure of their all-out efforts to block NATO's Euromissile counterdeployments through European public opposition to them.
And they would lose the kind of face Soviets hate to lose if they came back to arms control talks so soon after stalking out of them. Nor would Moscow want to do anything before next November to help reelect President Reagan.
Western diplomats therefore see the next ''window of opportunity'' for real movement in East-West relations as coming next November at the earliest, before a reelected Reagan is inaugurated (or a Democratic president-elect begins to formulate his foreign policy).
For this reason no Western chancellery thinks the West should volunteer concessions in nuclear arms control negotiations before that time.
Both European and American foreign ministries seem certain that some Soviet rethinking of East-West relations in a more constructive direction will eventually transpire.
They consider the Soviets to be realists and do not share the view of Columbia University professor Seweryn Bialer that Mr. Reagan's past condemnation of the Soviet ''evil empire'' might already have alienated them to the point where they would never do business with him.
(Reuters reports that Chernenko, in his acceptance speech following his election as secretary general, indicated he would give cautious support to economic changes introduced by Andropov.
(Chernenko praised the campaign against corruption and inefficiency and spoke in favor of an experiment in several industries aimed at giving more power to factory managers.
(But Chernenko sounded a note of caution that could prove significant in the long term. He declared his intention to carry out a major reassessment of the present policies, ''neither exaggerating them nor belittling them.'' Diplomats said this could lead to a major revision of Andropov's goals for industry and agriculture.
(Western diplomats suggested the economic reforms would depend to some extent on whether Chernenko allowed Politburo member Mikhail Gorbachev to retain overall control of them.
[Chernenko made no mention of foreign trade priorities, and Western economic attaches said they expected no changes in present policies.]