Israeli Prime Minister Menahem Begin said today that "there is reason to be optimistic about the peace talks that are about to start in Cairo.

Following U.S. Secretary of State Cyrus Vance's talks both with Begin and with Egyptian President Anwar Sadat over the past three days, U.S. officials say they never before seen so much flexibility and willingness to discuss the issues in the Arab-Israeli conflict as they found in Cairo and Jerusalem this week.

Optimism is also being expressed here that Jordan and Lebanon, and eventually Syria, will come into a snowballing peace process that started with Sadat's dramatic trip to Israel two weeks ago.

In a joint press conference with Vance this evening, Begin stressed that "we are now making a serious, real effort to achieve and establish peace in the Middle East."

American officials are underlinig both in public and in private the completely changed attitudes the Egyptians and Israelis are expressing toward each other. For the first time, the Americans say, both sides are suggesting ways to bridge the gaps between them, rather than using these differences as pretexts to block further discussion.

Vance has never seemed so relaxed and pleased about his Middle East diplomacy as on this, his third trip to the area as Secretary of State, according to those who accompanied him on his previous visits.

Neverthless, the Americans say they have no illusions that the many troublesome issues before the Cairo conference can be worked out overnight.

The Americans decline to gointo detail about how the Israelis and Egyptians conceive the actual negotiations in Cairo, but Israeli sources report differences in approach that in other, less euphoric time might have doomed such a conference to failure.

If the apparently sincere optimism of the diplomats is to be taken at face value, those differences seem simply to point to a lot of hard bargaining between negotiating partners who seek a deal.

The Israelis say the Egyptians told Vance that they want to open the discussions with three issues:

How the Palestinians can or should be represented in peace talks.

To what borders Israel will withdraw from the territories is conquered in the 1967 war.

What sort of timetable Israel is prepared to offer for its territorial withdrawals.

The Israelis say that their government first wants to discuss a "peace framework," meaning that they want answers to such questions as who will sign what peace treaties, whether ambasadors will be exchanged and so forth.

In the press conference, Begin referred to this approach in more general terms, such as setting down a set of pprinciples in Cairo that would guide an eventual overall peace settlement for all the parties to the conflict, not just Egypt and Israel.

Privately, the Israelis say they want to spend the opening phase of the Cairo confernce - generally considered likely to last until a Christmas recess seeing what the Egyptians have to offer.

Those with access to Begin's privately expressed thinking say, however, that even seems to have been personally caught up in the spirit of rethinking all his old positions, including his previous public inflexibility on territorial concessions.

Over the years, Begin has been among the hardest of the hard-liners on the question of returning lands to the Arabs that were traditionally Jewish in Biblical times. Many Israelis questioned whether Begin was personally capable of offering the kinds of concessions that the emotional and political breakthrough, created by Sadat seemed to call for.

"Now, Begin told reporters, "we meet, we talk. We shall go on meeting. We clarify matters, we make an effort, an intellectual effort all of us. And, therefore, there is reason to be optimistic."

Asked to elaborate his positions. Begin replied. "Give a chance to . . . negotiations. Everything will be negotiated. But the negotiations will take place in Cairo, in Geneva, in Jerusalem, with all the respect, not before the camera of our mighty friend, the television.

Although both Begin and Vance continued to stress that the negotiations are not meant to produce a separate peace, the Israeli leader hinted broadly that he is indeed interested in a peace treaty with Egypt that would serve as a "sample" for later treaties with Israel's other Arab neighbors.

"The delegations, both of Egypt and of Israel will deal." Begin said, "with the basic principles of the peace treaties to be negotiated concluded and ultimately signed. And, as you known under international law, there are many chapters and articles, sections and subsections of a peace treaty of very great value to the future of any nation which signs such a very important document of international standing and value . . . It will be a sample for the peace treaties to be signed with all our neughbors."

U.S. Officials said they they would expect Syria to come into the peace-making only at a much later time and that they would expect the Syrians to start out with a very hostile public position.

The Americans pointed out that the history of Middle Eastern negotiations, right from the foundation of Israel in 1948, has been that Egypt was the first to come to terms and that the others eventually followed more or less willingly.

The Americans here say they think Syrian President Hafez Assad genuinely believes that Egypt and Israel may cut a separate deal and that one of the useful American roles will be to try to persuade him that this is not the case. Egypt broke diplomatic relations with Syria last week over Syrian participation in the statement of the Arab conference in Tripoli, Libya, that Sadat has betrayed the Arab cause.

U.S. officials say they plan to urge the Syrians and others not to close their options.

The view here is that Saudi Arabia which has carefully refrained from comment on Sadat's actions, really decided to go along with Egypt, but that it will refrain from saying so because it wants to serve as a bridge between Egypt and Syria.

In the same view, Jordan's King Hussein is expected to join the Cairo talks, even without Syria, if he can possibly get through the political minefields between him and the negotiations.

As for Lebanon, the only think holding it break from peace talks with Israel is that it is under vitual Syrian military occupation, the analysts have concluded.

In what seemed to be a definite chance in tone from previous statements. Begin said that the "problem of the Palestinian Arabs" would be discussed in Cairo. He used the phrase "Palestinian Arabs" twice. Previously he has largely confined himself to explaining why he does not accept the term "Palestinians."

The Americans here say that they are satisfied that Israel is willing to come to grips with the Palestinian problem. Sadat has eased the way with his warnings to the Palestine Liberation Organization that it stands to be left out of the peacemaking and to be replaced by more moderate Palestinian spokesman if it continues to spurn the place set for it at the negotiating tables in Cairo and Geneva.

Meanwhile, in addition to the talks about to open on Wednesday in Cairo, parallel diplomatic channels seemed to be opening up between Israel and the Arab world. Egyptian Vice President Sayed Mubarak, now regarded as Sadat's closed foreign policy collaborator, announced that he is leaving Cairo for Paris to consult with the French government, not one of the leading actors in the current situation, for five days just as the Cairo talks open.

Simultaneously, Israeli Foreign Minister Moshe Dayan seems to be preparing to drop out of sight. He has put off an appointment Thursday with the visiting foreign minister of Belgium. It is now clear that when Dayan rushed home unexpectedly from a trip to Paris early this fall it was after a meeting in Paris with King Hassan of Morocco.

The King who served as the first serious Arab conduit between Begin and Sadat, was to have been visiting last week in the United States. He cancelled that trip as Middle East diplomacy was coming to a critical state.

"Paris is a very convenient place to meet people," remarked a diplomat who has spent large segments of his career going in andout of the French capital.

Vance goes on Monday to Jordan, then to Lebanon, Syria and Saudi Arabia, before returning to the United States at the end of the week.

Today, Vance took a break in his talks with Begin for a tour of the holy places in the Old City of Jerusalem. At Al Aqsa, the Dome of the Rock Islam's the third holiest place. Vance signed his name in the guest book directly under that of Sadat. The Egytian leader made Al Aqsa his first stop on his tour of Jerusalem.

Vance also visited the gold-domed Mosque of Omar, the Church of the Holy Sepuchre, the traditional site of Christ's crucifixion and burial and the Wailing Wall, the holiest Jewish site.