The Soviet Union will ask the International Olympic Committee to move the 1984 Summer Games out of the United States if the South African rugby team, the Springboks, is permitted to go ahead with a three-game United States tour scheduled to begin next Saturday in Chicago, The Washington Post has learned.

The Soviets, whose 1980 Moscow Olympics were the target of a U.S.-led boycott in protest against the Soviet invasion of Afghanistan, will formally make the request to move the Games out of Los Angeles at a meeting of the Olympic Congress beginning Sept. 22 in Baden-Baden, West Germany, if the Springboks play in the United States.

Meanwhile, Los Angeles Mayor Tom Bradley has asked the State Department, in a letter to Secretary of State Alexander M. Haig, to withdraw visas granted the South Africans for the tour. This followed by a day a letter from 65 political, labor and civil rights leaders to President Reagan urging the same action.

South Africa has been banned from Olympic competition since the mid-1960s because of the racial apartheid system practiced in that nation.

Col. F. Don Miller, executive director of the U.S. Olympic Committee, said he had no knowledge of the Soviet plans. But he said the USOC is opposed to the Springbok tour.

"We have heard indications from the International Olympic Committee that some Olympic nations from Africa would consider boycotting the 1984 Games if the Springbok tour goes on as scheduled," Miller said.

"In 1976, the Montreal Olympics were boycotted by 28 African nations because South African rugby teams had played in New Zealand, and then New Zealand played in the Olympics."

Rugby is not an Olympic sport, Miller said, and the U.S. Olympic Committee has no control over the Springbok tour.

The Springboks, said to be one of the finest rugby teams in the world, recently completed a two-month tour of New Zealand that sparked violent demonstrations at almost every game by people protesting apartheid in South Africa.

New York Mayor Edward Koch denied permission for the Springboks to play an American all-star team at the city-owned Downing Stadium on Sept. 26. Transferred to Rochester, the game was canceled by the promoter, who said that city authorities would not guarantee protection. Organizers subsequently announced it would be played at a secret location "somewhere in the northeastern United States."

Following the Sept. 19 game scheduled for Chicago, the Springboks are scheduled to play Sept. 22 in Albany. In Chicago, several organizations have announced plans to protest the Springbok game there, and a protest rally is scheduled for today.

Protesters have contended the South African government will use the Springbok tour to promote good will toward their country. Tour promoters argue it is simply a sports event with no political overtones.