It might still be only a glimmer in the eye of President Reagan's Middle East envoy Philip Habib. But if some American officials had their way, leaders of the main faction of the Palestine Liberation Organization (PLO) would end up living in Cairo under the moderating influence of Egypt.
As it is, a number of obstacles stand in the way of such a solution to the Beirut crisis. One is a potential veto from the PLO.
The idea of the PLO's main faction, Fatah and its leader, PLO chairman Yasser Arafat, ending up in Cairo, seems at first glance to be absurd. Egypt's late President Anwar Sadat alienated the PLO when he made his opening to Israel, and the PLO denounced the US-sponsored Camp David accords reached between Egypt and Israel.
But Egypt has always kept a few lines open to the PLO, and its new President, Hosni Mubarak, has reestablished some of the ties with the Arab world which had been broken or strained as a result of Camp David.
Egyptian officials recently met in Cairo with a high-ranking representative of the PLO. President Mubarak, for his part, meanwhile, has been calling for mutual recognition between the PLO and Israel and has described Mr. Arafat's recent assertion that he accepted United Nations resolutions relating to the Palestinians as a step in the right direction.
Reagan administration officials do not agree. They say that the Arafat statement amounted to a clever propaganda ploy. They also see some danger that Arafat may be overplaying his hand.
But what the Egyptians are proposing cannot be simply ignored. The fact that the Egyptians are willing to take in some PLO men gives them bargaining power. Egyptian officials are indeed saying privately that Egypt is ready to take in an undetermined number of PLO leaders and their followers. But they do not want to say this publicly until a package deal is agreed upon.
For one thing, they fear a PLO rebuff. They want the United States first to make a commitment to resolving the Palestinian problem in the direction of ''self-determination.'' Then, and only then, would the PLO leaders and their estimated 6,000 fighters leave Beirut. According to Arab sources, the fighters would go to several countries, including Syria, Jordan, and Egypt.
Arab diplomats seemed to be slightly encouraged by President Reagan's press conference comments made July 28. One diplomat pointed out that Mr. Reagan had not ruled out the possibility of a Palestinian state eventually being established on the Israeli-occupied West Bank of the Jordan River. Israel is firmly opposed to that idea. Reagan said the issue was ''up to the negotiators.''
President Reagan also set himself apart from the Israelis in another way. Israel has said that it will not negotiate with the PLO under any circumstances. Reagan was asked if he would welcome a move by the PLO toward talks with the US.
''Well, I think it would be a step forward in the process if the PLO would change the position it has had and that is that Israel must be destroyed - that it has no right to exist as a nation,'' the President responded. ''And what that would require is agreeing to abide by the UN Resolutions 242 and 338, agreeing that Israel is a nation and does have a right to exist.
''Then I would feel that the United States could enter into discussions with the PLO,'' he continued. ''I'm not speaking for Israel - that's up to them and we could not speak for them.''
Some Palestinian sources have indicated that it would be almost enough to get the PLO moving out of Beirut for the US to endorse a French-Egyptian plan for a new United Nations resolution. That resolution, now in the form of a draft, would recognize the ''legitimate national rights of the Palestinian people, including its right to self-determination with all its implications.''
As French and Egyptian sources explain it, this language would mean a Palestinian West Bank state. The US has never been willing to go this far, and Reagan administration officials have been cool to the French-Egyptian plan. The PLO, for its part, has been unwilling to endorse Resolution 242 - one of the resolutions mentioned by President Reagan - because it deals with the Palestinians only as refugees.
According to one American specialist on the Middle East, if Egypt's Mubarak can obtain the package deal that he envisages, ''it would buy Egypt entry back into the Arab world.''
Egypt's foreign minister, Kamal Hassan Ali, is currently visiting Washington. American officials say chances are good that he will get a chance to put the proposition directly to President Reagan before he leaves here.