Israel has given approval in principle to a controversial request by the United States to build a powerful transmitter in Israel for Voice of America radio broadcasts to the Soviet Union, senior Israeli officials said today.

The Israeli decision, which was made by Prime Minister Shimon Peres, Foreign Minister Yitzhak Shamir and Defense Minister Yitzhak Rabin, was conveyed to the Reagan administration by Rabin during his trip last week to Washington.

An Israeli official said the government here agreed to begin negotiations with the United States "with a view toward approving" construction of the transmitter in Israeli territory. He said the negotiations would center on technical questions such as the exact location of the transmitter and who will have operational control of it.

The technical negotiations are expected to begin in a matter of weeks and to last a few months, the official said.

The official added that Israel's "friendship with the United States" was the deciding factor in the decision, overcoming misgivings about the possible negative impact on the Jews of the Soviet Union and on the prospect of restoring Israeli-Soviet relations.

"We consider ourselves allies of the United States, and allies also give and don't just take," he said.

The Reagan administration's request last year to build a VOA transmitter here came during growing Israeli economic dependence on U.S. aid. Communications Minister Amnon Rubinstein, who also was involved in the government deliberations on the transmitter proposal, said that Israel was in no position to turn down the request, whatever its fears about possible negative consequences. Among the consequences that Israel fears is a further tightening of already severe restraints on Jewish emigration from the Soviet Union.

In December, sources here and in Washington said that the two countries were close to agreement on locating the transmitter in Israel. They said at the time that discussions had been under way for several weeks but cautioned that because the idea had attracted public attention, the timetable for reaching agreement probably would be set back. The Israelis, in particular, wanted the publicity to die down before acting on the U.S. request, the sources said.

In the earlier discussions, as an inducement to Israel, the United States was reported here to have suggested that Israel's state-run radio station, which has encountered jamming of its broadcasts to Soviet Jews, would be allowed to use the antijamming capabilities of the proposed VOA transmitter. An Israeli official said today that this suggestion may be part of the forthcoming negotiations on technical details of the agreement.

The Voice of America, which is part of the U.S. Information Agency, broadcasts worldwide. It is a key factor in the Reagan administration's effort to increase the flow of information about the United States to the Soviet people.

U.S. and diplomatic sources said earlier that the administration turned to Israel with the transmitter request after failing to persuade either Greece or Turkey, both members of the NATO alliance, to accept the transmitter.

Turkey, which has a border with the Soviet Union, reportedly feared that Soviet anger would subject it to reprisals and endanger its policy of maintaining cordial relations with Moscow as well as NATO membership.

Meanwhile, there have been increasing strains in the U.S. relationship with the Greek government of Socialist Prime Minister Andreas Papandreou. The disputes have included difficulty in negotiations over a new agreement for continued operation in Greece of two existing VOA relay stations that beam broadcasts to the Middle East and Southeast Asia.

In this atmosphere, sources said, the administration saw no chance that Greece would accept a new VOA facility for broadcasts to the Soviet Union.