Lebanon and Israel have agreed to begin face-to-face negotiations "in a few days," special Middle East envoy Philip C. Habib announced yesterday after reporting to President Reagan on his latest diplomatic efforts.

He said "some progress" already had been made toward an agreement on the withdrawal of foreign forces from Lebanon.

Habib's optimism about beginning the long delayed talks was reinforced by statements in Israel and Lebanon as officials in both countries scrambled to stake out public negotiating positions.

Israeli Army radio reported that the talks could begin in the next three days, and in Beirut, Prime Minister Shafiq Wazzan told reporters that the Israeli government had passed the word that it wanted the negotiations to start "soon and perhaps before Christmas."

Habib, in a statement read by White House deputy press secretary Larry Speakes, said no location had been set for the talks. Sources in Beirut told The Associated Press that the Lebanese government was leaving the choice to the United States.

Middle Eastern diplomats in Washington said that there have been discussions about holding them alternately in Khaldah, a suburb of Beirut now held by Israel, and in Qiryat Shemona, an Israeli kibbutz village just south of the Lebanese border.

On Sunday, the Israeli Cabinet dropped its condition that some of the talks be held in Jerusalem. That had been the principal stumbling block to beginning negotiations. Lebanon had balked at sending negotiators there, fearing that their presence could be interpreted as recognizing Israel's disputed claim that Jerusalem is its capital.

The Israeli Cabinet's change in position came after a week of exertions by Habib and his colleague, Morris Draper, who shuttled back and forth between Beirut and Jerusalem in an effort to break the logjam after it became clear that the Israelis and Lebanese were making no progress on their own.

Reagan, who had previously announced the goal of getting foreign forces out of Lebanon by the end of the year, expressed the hope yesterday that the talks would be completed "swiftly and successfully," Speakes said. Reflecting that optimism, one U.S. official said that much of the fine print of a withdrawal agreement already had been tentatively agreed upon in discussions the United States has conducted with Israeli and Lebanese officials during the past three months. Other U.S. officials were not as hopeful, however, saying there are still many thorny issues to be resolved.

The rough agenda of topics to be covered in the talks, U.S. sources said, includes troop withdrawal, security arrangements along the Lebanon-Israel border, trade and economic relations and the kind of political ties that will be established between the two countries.

Israel had been insisting on free trade, open borders, permanent mountaintop watchposts in central Lebanon, control of air navigation and shipping and rights to divert some of the waters of Lebanon's Litani River to northern Israel. According to press reports from Beirut, Lebanese President Amin Gemayel told visitors last week that he considered those demands "unreasonable and unacceptable."

Lebanon has indicated a willingness to make some kind of security arrangements with Israel but has been concerned about signing any agreement that would appear to be a peace treaty, fearing that would jeopardize Lebanese relations with other Arab states. Lebanese officials also have indicated an unwillingness to enter into any economic relationship with Israel, and they have complained that Israel flooded Lebanon with agricultural goods and other products following the June 6 invasion.

Left unclear yesterday was just what assurances Habib may have received from Syrian and Palestine Liberation Organization forces that they will leave Lebanon. Both have indicated a willingness to depart after Israeli forces do so and those assurances were reiterated in news accounts in the Middle East yesterday.

In an interview in a Lebanese magazine published yesterday, Khaled Fahoum, speaker of the Palestine National Council, the PLO's parliament-in-exile, said, "We are willing to cooperate with President Gemayel and shall abstain from giving the Israeli enemy any pretext to remain in Lebanon."

The Kuwait newspaper Al Qabas quoted Syrian President Hafez Assad as saying he had "assured" Gemayel that Syrian forces would partially pull out of the Bekaa Valley by the end of the month.

Israeli Defense Minister Ariel Sharon told a committee of the Knesset, or parliament, yesterday that Syria had agreed to the first phase of a mutual withdrawal from Lebanon. But he added that there would be no Israeli withdrawal unless Syria released all Israeli prisoners of war and returned the bodies of Israeli soldiers killed in the fighting.