President Carter's special Mideast negotiator said yesterday he believes "there is a resonable possibility that Israel and Egypt will meet their May deadline for agreement on a selfgoverning authority for the Palestinian inhabitants of the Israeli-occupied West Bank and Gaza Strip.

Sol M. Linowitz, who returned last Thursday from talks with Egyptian President Anwar Sadat and Israeli Prime Minister Menachen Begin, said he was more encouraged than before his trip that the two sides are negotiating in good faith and are trying to meet the May deadline.

Under the Egyptian-Israeli peace agreement, the governments are pledged to negotiate an accord giving limited self-government to the West Bank and Gaza inhabitants for five years. That is intended as an interim period during which the ultimate status of the areas will be determined.

Linowitz, who took over the mediator's job from Robert S. Strauss last month, conceded that major disagreements still exist on such key questions as control of water supplies and land rights and Israel's demand for security measures in the occupied territories.

But, he added, the negotiations have produced greater progress than he had been aware of on such matters as the self-governing authority's powers in education, transportation, health and agricultural and industrial development.

As to the continuing reluctance of the Palestinian inhabitants to join the negotiations, Linowitz said: "If I were a Palestinian . . ., I don't think I would be very interested in joining these negotiations at the moment.

"I would ask, "What's in it for me?' and I wouldn't be sure of the answer," he said. But he added: 'The challenge is for us to fashion a credible, viable system which would be attractive to the Palestinians and that will make them want to join and become participants."

Referring to his experience as one of the negotiators of the Panama Canal treaties, Linowitz said: "I think we should try to do what we set out to do in the Panama Canal talks -- to come up with a set of proposals that we'll be proud to show the world.Then it's up to the other parties to decide what they want to do."

Linowitz said he does not expect to return to the Middle East until after a meeting between Sadat and Begin next month. He said he has been in contact with King Hussein of Jordan and hopes, perhaps on his next trip, to meet Hussein in an effort to convince Jordan it should join the talks.