Although the Israeli government says it is pushing ahead with a formal investigation into allegations that Israeli agents recruited and used an American citizen as a spy in the United States, officials here have begun to suggest that the affair is already close to being resolved without any damage done to American-Israeli relations.

Some officials indicate, in response to questions, that the strategic relationship the two countries have built up in recent years would be spared any further strains by a quick guilty plea from the accused spy, Jonathan Jay Pollard.

Pollard, 31, a civilian counterterrorism analyst for the U.S. Navy, was arrested Nov. 21 on charges of selling U.S. military secrets to Israel.

In the four days since Secretary of State George P. Shultz and Israeli Prime Minister Shimon Peres held a lengthy telephone conversation about the Pollard case, leading Peres to issue a formal statement of apology, Israeli officials have begun to decline to talk about any details of the affair and to confine themselves to minimizing its importance.

In the view of senior Israeli officials who are intimately involved with U.S.-Israeli relations, the limits of American patience with Israel have not been stretched even marginally by the allegations against Pollard and the public criticisms of Israel issued by the State Department last week for an alleged lack of cooperation.

The officials said that they expected some residual publicity on the case but that basically they consider the issue dead.

One Israeli official, with a background of 12 years of close involvement in U.S.-Israeli relations, called the disclosures of Israeli espionage in Washington a "blip on the Richter scale" compared to other occasions since 1967 when Israeli and U.S. interests collided.

"This is not even a serious crisis," said the official. "It is just a juicy story."

Citing their concern for U.S. sensitivities during a delicate phase of efforts to lower the temperature of the controversy, the officials spoke on the condition that they not be identified. However, their views represent both the Labor and Likud factions of the national unity coalition government, and they mirror, to an extent, widely held attitudes in the Israeli public.

The officials' comments reflected a frequently encountered view here that the United States is as dependent on Israel for meeting its strategic objectives in the region as Israel is dependent on the United States for financial and political support.

Or, as one official put it succinctly, "We know the Americans don't give us all that money because they like our beautiful blue eyes." He said the spy case should be considered a "pitfall" rather than a crisis in U.S.-Israel relations.

Among the incidents he cited as embarrassing to both governments was the Israeli attack on the American intelligence ship, the USS Liberty, at the outset of the 1967 Arab-Israeli war.

A total of 34 American lives were lost when Israeli jets attacked and heavily damaged the U.S. electronics surveillance ship off the Sinai Peninsula two days after the start of the war. The attack also wounded 164 Americans.

In the case of the Liberty, it apparently was Israeli suspicion of American spying that triggered the attack. There were charges that Israel ordered the attack in the belief that the U.S. ship jeopardized the surprise element of Israeli military moves. Israel claimed that its pilots had mistaken the Liberty for an Egyptian ship.

After a military inquiry, Israel expressed regret and offered to pay compensation to the victims.

Compared to something like the Liberty attack, "the Pollard matter is something on the range of a skirmish -- a very short pitfall, indeed," the official said.

The Israeli officials insisted that they were not intimidated by the sharply critical statement issued last Friday by the State Department saying the Reagan administration was "dismayed" at a lack of Israeli cooperation. They said that Shultz's telephone call to Peres at 3:30 a.m. Sunday (Israeli time) gave more impetus to Peres' decision to issue a public apology than did the statement by State Department spokesman Charles E. Redman.

During the telephone conversation, Israeli sources said, Peres agreed to allow U.S. Justice Department officials to question Rafael Eitan, who has been named as the head of the Israeli scientific research office that recruited Pollard, and the two Israeli diplomats who were recalled to Israel after Pollard's arrest.

Another senior Israeli official said that the U.S.-Israeli bond that overshadows such bilateral crises goes not only to the policies of the two countries and a shared strategic interest in blocking Soviet expansionism in the Middle East, but also to a close personal relationship between Peres on the one hand and President Reagan and Shultz on the other, as well as to a "close affinity of U.S. public opinion and the U.S. media to Israel."

As an indication that bilateral relations have not been affected by the spy scandal, Israeli officials said today, the Reagan administration had not asked to postpone the biannual meeting now under way in Washington to discuss the U.S.- Israeli strategic cooperation agreement.

"The mere fact that we are continuing the strategic cooperation talks indicates that, at least in this area, contact is continuing at the highest level of exchange," an Israeli Foreign Ministry official said. He noted that the strategic talks involve an exchange of sensitive intelligence data.

The official also said that all intelligence-related meetings between U.S. officials and Israeli diplomats in Washington that had been scheduled before the Pollard case surfaced have taken place without interruption.

In a sense, the central figure in the controversy, Pollard, has been lost in the diplomatic scrambling to apply damage control to U.S.-Israeli relations.

Since the official Israeli position is that the alleged Washington espionage network was a "mistake" committed by an unauthorized, free-lancing intelligence unit unknown to the ministerial level of government, the outcome of the prosecution of Pollard should not affect U.S.-Israel relations adversely, officials said.

But some Israeli officials said they hoped that Pollard would plead guilty and that the sustained adverse publicity a trial would bring could be avoided. They said the government, having publicly washed its hands of the intelligence unit that allegedly handled Pollard, hardly could come publicly to the defense of the former civilian naval analyst.