Administration officials said yesterday that they expect a summit meeting between President Reagan and Soviet leader Mikhail Gorbachev this fall in Washington or New York.

The officials emphasized that no date or place for a summit had been set and said further diplomatic exchanges are needed before a meeting can be arranged. But they said one possibility is a meeting in October if Gorbachev attends a special observance commemorating the founding of the United Nations. The observance is scheduled for Oct. 24, United Nations Day.

In an interview Monday with reporters for The Washington Post, Reagan said Gorbachev had replied to his invitation for a summit meeting in Washington; other officials termed the reply positive but said the new Soviet leader had not designated a date or place.

At a White House departure ceremony yesterday for Turkish Prime Minister Turgut Ozal, a television reporter shouted a question to Reagan about the summit meeting, asking: "Whose court is the ball in?"

"Theirs," Reagan replied.

Pending a more specific Soviet reply, administration officials tried publicly to dampen summit expectations yesterday.

"There are no negotiations for a summit," White House spokesman Larry Speakes said. "There have been no discussions about arrangements for a summit, no meeting set, no time set -- nothing along those lines. Nothing has taken place now and I don't know of any specific plans for any meetings or arrangements."

Nonetheless, officials who spoke on condition they not be identified were optimistic about prospects for a summit. Reagan said in the Monday interview that he was "hopeful" such a meeting would take place.

U.S. and European officials said it was unlikely that Reagan and Gorbachev would meet in Helsinki this August when officials gather to commemorate the signing of a human-rights accord there in 1975 by 35 nations, including the United States and the Soviet Union.

European diplomats expect that Gorbachev will make his first Western trip since assuming the Soviet leadership this summer, probably visiting Paris. He is expected to travel to New York this fall to address the United Nations.

Some officials consider Gorbachev more likely to attend the observance of the U.N.'s founding in October rather than the opening of the General Assembly in mid-September.

A summit with Reagan, either here or in New York, presumably could take place afterward.

Officials said it probably would be wide-ranging and not limited to a discussion of nuclear weapons, which the superpowers are negotiating in talks in Geneva.

Discussing the strategy of both sides in these talks, U.S. Ambassador Edward L. Rowny said Monday that the Soviets were "diverting attention" from U.S. efforts to limit offensive nuclear weapons by concentrating on Reagan's advocacy of a missile defense system.

"Rather than allow the Soviets to divert attention from this objective of limiting offensive weapons by focusing on the defense and space issue, where systems don't even exist, we should work at reaching agreements aimed at reducing nuclear arms, which do exist," said Rowny, a special adviser to the president on arms control.

Reagan said last week that the ultimate impact of his defense proposal, known as the Strategic Defense Initiative, would be to make offensive nuclear weapons more negotiable.