WASHINGTON--Soviet President Mikhail S. Gorbachev will meet with President Reagan and President-elect George Bush next month, the White House announced yesterday.

Spokesperson Marlin Fitzwater said that neither a date nor a site has been set for the meeting, although he acknowledged that it would likely take place in New York while Gorbachev is there to address the United Nations General Assembly.

Other officials, requesting anonymity, said Gorbachev would probably meet with Reagan and Bush on December 7.

Fitzwater said Reagan and Bush would meet, probably together, with Gorbachev, but said the session would not be "a summit in the sense of a summit."

"It would, rather, be a cordial meeting between superpower leaders reflecting the friendship they have created and the historic change in the relationship between the United States and the Soviet Union," he said.

Fitzwater said the main purpose of the meeting from the U.S. standpoint would be to "ensure that the momentum and continuity of the arms control talks are extended and...reaffirm the relationship between the general secretary and the new President of the United States."

"I would not look to it as a meeting that would be settling [differences]," Fitzwater said.

Fitzwater acknowledged that the Kremlin had proposed that Gorbachev meet with Reagan and Bush in just the last few days and that the administration had agreed.

The meeting with Reagan around December 7 would give the two sides another chance to narrow the gap on a treaty to reduce long-range nuclear weapons arsenals and to ease tensions caused by rebel attacks on Soviet troops in Afghanistan and a slowdown in the Red Army's withdrawal from the country.

The treaty is bogged down with several technical problems that may not be easily solved. But on Afghanistan, the Soviets already have pledged to have all their forces out by February 15.

Two weeks ago, citing attacks by the U.S.-armed rebels, the Soviets announced suspension of the withdrawal. Still, Gorbachev has not ruled out adhering to the deadline set in last spring's Geneva accords.

Two members of the Senate Foreign Relations Committee said yesterday that a meeting during the United Nations session could also give Bush the chance to build on recent positive Soviet moves around the world.

Interviewed yesterday, Sen. Joseph Biden (D-Del.) pointed to "some of the moves taking place in the Soviet Union, and its affect on Europe in particular and the Third World in general," and said the New York meeting would give the president-elect "a significant opportunity...to take positive advantage" of them.

Sen. John F. Kerry (D-Mass.), interviewed with Biden on the NBC-TV "Today" show, said Bush "has a number of fronts where there are major opportunities. Clearly, the Soviet Union and east-west relations is one, moving on human rights, trade, regional conflict resolution and arms control."