U.S. Trade Representative William E. Brock briefed President Reagan yesterday on whether to continue restrictions on shoe imports from Taiwan and Korea, an issue that again will test the administration's free-trade philosophy.

The president, who made no decision yesterday, must determine the future of orderly marketing agreements imposed during the past three years on footwear from Taiwan and Korea. The International Trade Commission recommended keeping restrictions on Taiwanese imports for another two years, except on athletic footwear, and eliminating restraints on shoes from South Korea.

The orderly marketing agreement expires at the end of this month, and Reagan must make a decision before then, an administration official said.

William A. Niskanen Jr., a member of the Council of Economic Advisers, told reporters yesterday the president has been given a wider range of options than just extending or eliminating the orderly marketing agreements.

The agreements didn't help the domestic industry and only led to higher-priced and lower-quality shoes for women's and children's shoes, Niskanen said. He added that the American footwear industry is in "Pretty good shape," partly because during the past several years, many firms consolidated and small businesses dropped out.

The Taiwanese have suggested allowing the quotas to expire for both countries and replacing them with an import-monitoring system having an antisurge device to control any unexpected serious competition for domestic shoemakers.

House Speaker Thomas P. O'Neill of Massachusetts and a group of congressmen have asked for a three-year extension of restrictions on shoe imports from both countries. They said the 127,000 workers in the American shoe industry are low-paid and that shoe imports continue to threaten the domestic industry.

The congressmen said if restrictions are removed from Korea, it could take over the shoe-import market left open by Taiwan.

The ITC ruled that Korea, a major athletic-shoe exporter, no longer threatens U.S. producers. But the commission added that Taiwan's producers of regular shoes could threaten domestic shoemakers. Taiwan and Korea last year had 50 percent of the U.S. shoe import market compared with 61 percent before the orderly marketing agreements.