The Reagan administration does not expect the departure of Israeli Prime Minister Menachem Begin, whether now or in a few months, to cause much change in a U.S.-Israeli relationship that is currently good but has a built-in potential for sudden swings back to suspicion and strain.

The White House and the State Department reacted yesterday to Begin's proposed resignation with statements that it is "an internal Israeli matter" on which they would have no comment.

In private, U.S. officials said they believe his successor, tentatively expected here to be Foreign Minister Yitzhak Shamir or Deputy Prime Minister David Levy, to continue the aggressive, hard-line policies associated with Begin.

That, the officials said, would continue the dichotomy in the relationship that has seen the Begin government seek to keep U.S. military, economic and diplomatic support so vital to Israel, while simultaneously maintaining a tough, no-quarter stance toward the Arab world that frequently is in conflict with wider U.S. interests.

In the U.S. view, the main differences are likely to involve style and personality. None of Begin's potential successors has his almost mythic stature within Israel, and U.S. officials believe a new prime minister will be unable to govern in the autocratic, paternal manner that has been his hallmark. But, the officials stressed, whether that will help or hinder U.S. efforts to influence Israel's course is unclear.

Former president Jimmy Carter, who brought Begin and Egyptian President Anwar Sadat together at Camp David, said Begin's resignation would not affect prospects for future Middle East settlements.

A new prime minister would not radically shift Israel's policies toward its neighbors or the United States, Carter said in Atlanta.

"I think the basic interrelationships between our country and Israel are overwhelmingly based on mutual concerns and mutual interests," Carter said. "And, of course, Prime Minister Begin will have a major voice in his party's affairs in the future, even though he's not prime minister."

In Vail, Colo., former president Gerald R. Ford said he hopes Begin's successor will work more assertively for peace than Begin had. He said Begin's unwillingness to scrap plans for further West Bank settlements has had "an adverse impact on peace."

Ford added that any successor should "push in a constructive way" for President Reagan's peace plan.

The timing of Begin's announcement yesterday caught the administration by surprise. But since the death of his wife last winter, U.S. officials have been working on the assumption that Begin, 70, his interest in power dulled by grief and poor health, wants to step down. Even if he is dissuaded from resigning now, officials here expect that he will be postponing his retirement only for a few more months.

Begin's departure now would mean a change in Israeli leadership as the U.S.-Israeli "special relationship" has weathered tensions besetting it only a few months ago and regained much of its former friendly spirit.

As recently as last spring, the two governments appeared to be on the most serious collision course in the 35 years since the United States became the first nation to recognize Israel's independence. At issue then were U.S. anger at Israel's continued occupation of Lebanon and Begin's bitter hostility toward President Reagan's Middle East initiative calling for Israeli-occupied Arab territories to gain independence "in association with Jordan."

A confrontation was avoided largely because of continuing divisions in the Arab world. First, failure of Jordan's King Hussein and the Palestine Liberation Organization to agree on a response to the Reagan initiative put that idea in limbo and removed the U.S. incentive to prod Israel for flexibility on the occupied territories.

Then Israel cooperated with Secretary of State George P. Shultz's shuttle diplomacy and reached agreement with Lebanon on withdrawal of Israeli forces.

The accord foundered because of Syria's subsequent refusal to pull out its forces, with the result that an Arab government, rather than Israel, became the impediment to a Lebanon solution.

While a renewed atmosphere of mutual good feeling has been evident in the relationship throughout the summer, there have been signs recently that a mercurial new shift could be near.

The Israelis are suspicious that Reagan's new special Mideast envoy, Robert C. McFarlane, might seek further Israeli concessions in Lebanon as a means of finding a withdrawal formula acceptable to Syria.

In his radio address Saturday, Reagan signaled a possible U.S. push to revive his peace initiative and coupled it with surprisingly strong criticism of the "unhelpful" nature of Israel's insistence on building new settlements in the occupied territories.

It is too early to tell whether the administration is cranking up a new attempt to pressure Israel in Lebanon or the occupied territories. White House press secretary Larry Speakes, speaking with reporters yesterday in Santa Barbara, turned aside questions about Begin and sought to focus on what he called "encouraging" signs that McFarlane is making progress in efforts to prevent a major escalation of civil war between feuding Christian and Druze Moslem factions in Lebanon.

McFarlane is in Paris talking with Druze and Lebanese government representatives about an agreement that would permit the Lebanese army to take control in the Chouf Mountains after Israeli forces leave the area for new positions in southern Lebanon.

Speakes said the United States "anticipates" that McFarlane's mission will not be affected by Begin's announcement and added: "We expect him to continue to receive full cooperation from the Israelis."

That view was echoed by other U.S. officials here. They noted that Shamir and Defense Minister Moshe Arens comprise a Cabinet power center that has argued successfully since last spring for maximum possible cooperation with the United States on Lebanon, and that attitude is expected to continue whether or not Begin remains.

The administration privately would prefer to see Arens, formerly Israeli ambassador here, succeed Begin, although that is not possible now because he is not a member of the Knesset (parliament). However, he is expected to remain a strong influence, and many believe that he is likely to emerge after a transitional period as prime minister and leader of Begin's Likud bloc.

U.S. officials also believe there is now little chance that Ariel Sharon, forced out as defense minister after last September's massacre of Palestinians in Beirut, can mount a bid for power. They note that Sharon was the architect of the Lebanon invasion, and public opinion within Israel appears to have soured toward that venture.

As a result, the administration believes that, if Begin leaves, the Israeli government will still be controlled by those committed to cooperation with Washington on immediate problems such as Lebanon.

But, in regard to more long-range issues such as the future of the occupied territories, Shamir, Arens and Levy fully share Begin's view that the West Bank and Gaza Strip should remain under Israeli control.

And, U.S. officials noted, if the Likud retains power as expected, the United States can anticipate continued trouble with Begin's successors in tackling the larger questions regarding Palestinians and a comprehensive solution to the Arab-Israeli conflict.