Soviet diplomats secretly have told almost every major American Jewish organization over the last year that there is a possibility of Moscow restoring diplomatic relations with Israel and allowing greatly increased numbers of Soviet Jews to emigrate to Israel by next spring, representatives of the organizations said yesterday.

The Jewish groups, however, have tended to be skeptical about the predictions, most of which were made in contacts initiated by officials of the Soviet embassy here, according to the organization officials, who asked not to be identified.

The representatives said the dominant feeling among people active in efforts to aid Soviet Jewry is that the Soviet Union has been engaged in a campaign to improve its image in this country. They added that the Soviet approaches have been reported to the Israeli government and said Jerusalem appears to share the view that the Soviet effort probably is a public relations ploy rather than a signal of a major policy shift.

Specifically, the sources said, Israeli officials and American Jewish leaders believe Moscow wants to take advantage of tentative moves toward better U.S.-Soviet relations to obtain trade advantages denied it by Congress because of Soviet restrictions on emigration by Jews and other citizens.

The representatives said the Soviets seem to think their chances will be improved if they can induce Jewish organizations here to lessen their use of newspaper advertisements and other means of publicizing the plight of Soviet Jews.

In addition, the representatives continued, many of the people who were involved in these contacts have come away with the impression that the Soviets have what one called "a very unsophisticated view of American Jewry and are trying to fish out the individuals and organizations that control the Jews in this country."

"They seem to have the idea that Jews have enormous influence over government policy and public opinion," he added. "As a result, they appear to believe that if they identify the people who, by their lights, run Jewish affairs in this country, they can play up to them with promises of big things to come and induce them to mute criticism of Soviet policy."

Representatives of various Jewish groups disclosed the year-long pattern of Soviet contacts after The New York Times reported yesterday that a Soviet diplomat last week told a Washington representative of the Los Angeles-based Simon Wiesenthal Center that he believes Moscow will move in February to restore relations with Israel and relax restrictions on emigration of Soviet Jews.

Rabbi Abraham Cooper, associate dean of the center, confirmed in a telephone interview yesterday that the meeting took place here last week. Cooper said officials of the Los Angeles center regarded the contact as "significant," but he also noted, "We are unable to say whether it was only a continuation of an ongoing series of smoke signals and disinformation or whether it was a sign that we are headed for a real breakthrough."

However, officials of other American Jewish organizations said that while the Wiesenthal center was the first to reveal such an approach publicly, it was not the first group to be contacted in that fashion. Instead, the sources said, beginning last January, various Soviet diplomats have engaged in what one source called "a seemingly systematic run-through" of contacts with almost all of the secular and religious groups that belong to the Leadership Conference of Presidents of Major American Jewish Organizations.

In every case, the sources said, the Soviet diplomats who made the approaches talked of a time frame centering on next spring. But, the sources added, in each instance, the Soviets were careful to qualify their predictions heavily by using such terms as "maybe" or "if U.S.-Soviet relations continue to improve . . . ."

In some cases, they added, the Soviet diplomats implied that possible policy changes by Moscow might be linked to Israeli willingness to permit participation by the Soviet Union and Syria in moves toward renewed Middle East peace talks. But, the representatives continued, the Soviets appear to have dropped that line in their recent approaches, and Cooper said it did not come up in the approach to the representative of the Wiesenthal center.

Initially, the representatives said, the Soviet efforts stirred considerable interest in American Jewish circles. They said that for a time the Soviets seemed to be focusing special attention on Edgar Bronfman, head of the World Jewish Congress, who delivered a letter from Israeli Prime Minister Shimon Peres to Soviet leader Mikhail Gorbachev during a September trip to Moscow.

Despite official Israeli denials that Bronfman was acting as their intermediary, there have been persistent rumors that he was engaged in secret negotiations about plans to airlift Soviet Jews to Israel from Poland or other European countries. According to Jewish-American leaders, though, Moscow's failure to make any gestures about Jewish emigration at last month's Geneva summit between Gorbachev and President Reagan have dampened greatly expectations here and in Israel that any major changes can be expected from Bronfman's efforts or the various other contacts.

Washington Post correspondent William Claiborne reported yesterday that Israeli officials in Jerusalem are insisting they see no tangible signs of a Soviet policy shift of the type described to the Weisenthal center. The Israeli officials added that even if the Soviets were contemplating a shift, it seems unlikely that Moscow would choose to reveal such a major reversal through an unidentified first secretary in the Washington embassy.