Egypt will seek a new U.N. Security Council resolution on the Middle East that would keep existing resolutions as the basis for a regional peace settlement but add provisions calling for self-determination for the Palestinians and the right of the Palestinians to a homeland, Cairo newspapers reported today.

If adopted, such a resolution could provide the basis for talks between the United States, which has opposed any changes in the existing resolutions, and the Palestine Liberation Organization, which refuses to accept them.

If the United States supported a new solution such as that suggested by Egypt, or even allowed it to pass by abstaining, it would mean a split with Israel that the Arabs would see as a major breakthrough, diplomatic analysts said. The newspapers here, which usually reflect official thinking on foreign affairs, said Foreign Minister Ismail Fahmi and President Carter discussed the proposal during their meeting in Washington yesterday.

The Carter administration has already displeased Israel by saying there must be a role for Palestinians in the search for a regional settlement. But Washington has refused to deal with the PLO unless it accepts U.N. resolution 242, adopted in 1967. That resolution implies the right of Israel to exist as a state. The PLO opposes it on the grounds that it refers to the Middle East's "refugee problem" but says nothing of the Palestinians or their national rights.

The Egyptian formulation would bridge the gap between those two positions. Accounts in the Arabic language press aid it would call for the creation of a Palestinian "watan," which is usually translated as homeland. Diplomats here pointed out that it would be difficult for the United States to veto such a resolution since Carter himself has used that word in outlining his vision of a settlement.

Carter has asked the Palestinians to accept Resolution 242 as the means of opening a dialogue with Washington. He said the Palestinians were free to express any reservations about the resolution but would have to declare their acceptance of its principles.

The PLO refused because the United States would not guarantee them an invitation to a new Geneva accepted, so they would have given away their most important bargaining chip, recognition of Israel just to talk to the Americans.

PLO leader Yasser Arafat has already said he could accept Resolution 242 if it was modified by the Security Council along the lines Egypt is now suggesting.

From Egypt's standpoint, such a resolution would have the advantages not only of driving a wedge between the United States and Israel but also of bringing the PLO more firmly away from Syrian tutelage into the American-oriented camp headed by Egypt and Saudi Arabia.

It was also reported today that Fahmi will offer proposed formulas for getting around the Israeli refusal to accept the PLO at Geneva. One suggestion is that Palestinians who are not PLO members be permitted to take part as members of a unified Arab delegation and that the PLO be permitted to choose the delegates. Israel, however, is opposed to the idea of a unified Arab delegation as well as to the PLO.

Despite the flurry of negotiations and apparent progress over these procedural matter, the prevailing view here appears to be that there can be no breakthrough toward peace until the United States forces Israel to give ground on the two points where it has been inflexible - a complete withdrawal from the territories captured in the 1967 war and autonomous Palestinian state.