The United States has suggested to Israel that the Palestine Liberation Organization could retain a political presence in Lebanon as part of a peaceful solution to the Israeli siege of Beirut, Israeli radio reported tonight.

This was a point on which Washington could differ at least in nuance from Israel in efforts to organize a departure of PLO guerrillas from Lebanon and avert an Israeli assault on their surrounded strongholds in West Beirut, the government-run radio said. It was contained in a message from outgoing Secretary of State Alexander M. Haig Jr. that the broadcast said generally reaffirmed U.S. support for the Israeli action in Lebanon and its political goals there.

With the principle of departure reportedly accepted by the PLO leadership, bargaining over such details was said to be under way again today in exchanges between PLO leader Yasser Arafat, Lebanese political personalities and, through them, the United States and Israel. Details, Page A23

In what was interpreted as a gesture of optimism, Prime Minister Menachem Begin's Cabinet held a special session today and, the radio said, decided to allow U.S. envoy Philip C. Habib another few days to work out details of a settlement acceptable to Israel and the Palestinians.

In a parliamentary debate last night, Begin said he would give Habib only "a day or so" to win agreement before ordering an attack by Israeli forces ringing the beleaguered guerrillas in Beirut's Moslem sector.

Israeli troops seen on a drive through their positions around Beirut today appeared relaxed and there were no signs that preparations for such an attack were under way. At the same time, any such assault likely would be preceded by more bombing by Israeli warplanes and shelling by heavy artillery already set up around the Lebanese capital.

It was unclear whether the question of a political PLO presence in Lebanon has become a major sticking point in the talks. High Israeli officials until now have insisted that all the estimated 6,000 PLO fighters in Beirut must leave "without any exceptions."

After this is accomplished, a Lebanese government with restored sovereignty could then decide to allow the PLO to open an office in Beirut similar to those the organization runs in such European capitals as Vienna or Paris, a senior official suggested. This would be acceptable to Israel so long as the office remained under Lebanese control and did not take the shape of renewed military presence on Israel's northern border, he added.

The PLO already operates such an office in Beirut, headed by Shafiq Hout, the unofficial PLO ambassador to Lebanon. Because of the heavy guerrilla presence in Lebanon, many Lebanese officials have become used to dealing directly with Arafat or his top lieutenants, and the office lost some of the importance it might otherwise have had.

The United States is believed to have something similar to the Israeli position in mind. But it was not known whether Haig, in his guidelines for Habib's talks in Beirut, also has specified that a political presence could be possible only after all PLO guerrillas now in Beirut depart for another country.

Although Israel's position on the issue was described as non-negotiable, U.S. bargaining or pressure could bring a shift. At least one previous position described as immutable by high Israeli officials has been softened by Begin.

The Israeli leader said last night that PLO guerrillas could leave with their personal arms, presumably pistols and AK47 assault rifes, the standard PLO guerrilla weapon. Only hours before Begin's address to the parliament, or Knesset, a senior official involved in the exchanges with Habib had insisted they could leave with only "their lives."