An exchange of American and Soviet professors, annual tournaments of U.S. and Soviet athletes and joint cancer research are among the ideas approved last week by President Reagan and Soviet leader Mikhail Gorbachev in a little-noticed facet of their Geneva summit.

State Department officials said yesterday that programs approved at the summit are a start on more extensive people-to-people exchanges proposed by the administration in a diplomatic message to Moscow a month ago and announced by Reagan in a Nov. 14 address shortly before leaving for Geneva.

U.S. and Soviet elementary-school students visiting one another's summer camps as well as joint television programs to bridge the geographical and ideological distance through electronics are among the additional programs most likely to be approved soon, the officials said.

Those two proposals were suggested by Moscow in a Nov. 12 diplomatic message, reacting to the earlier suggestions from Washington, and were accepted by the United States at the Geneva meeting, according to the sources. But when it came time to approve the final draft of the joint statement to be issued by Reagan and Gorbachev, the Soviets insisted that their own proposals were too specific to be issued under the imprimatur of the two top leaders.

The most ambitious item suggested by the United States, the exchange of up to 5,000 university undergraduates in each direction, was not accepted by Moscow, even after Washington pared down the number to 300 each way in a pre-summit compromise. But State Department officials expressed hope that a broad exchange of undergraduates might develop in time if smaller programs prove productive.

The six people-to-people programs approved by Reagan and Gorbachev, and endorsed in their final statement Thursday morning, are:

*An annual exchange of professors to conduct "special courses in history, culture and economics" in U.S. and Soviet universities. The proposal under discussion before the summit called for five to 10 professors going in each direction for a semester or an academic year.

*A U.S.-Soviet scholarship program for "the best students" from each country in natural sciences, technology, social sciences and humanities to make possible exchanges for an academic year. About 10 students from each side would be exchanged in what an official called a smaller, Soviet-American version of Rhodes scholarships, which offer students in the United States and British Commonwealth countries two- or three-year periods of study at Oxford University.

*Promotion of Russian-language studies here and English-language studies in the Soviet Union. One idea under consideration, officials said, is the expansion of an existing summer program that allows American teachers of Russian, who number about 2,000 to 2,400 nationally, the chance to visit the Soviet Union.

*A joint program of cancer research. The details of this item are particularly uncertain because it was a personal project of Reagan, who had a cancer operation this year, that he undertook without much bureaucratic assistance, officials said. A U.S. health specialist said it is unclear how much benefit can flow from a joint U.S.-Soviet cancer-research program because, "We probably don't have that much to learn from them."

*Cooperation in development of educational exchanges and software-related computer instruction for elementary- and secondary-school students. The United States is insisting that people be exchanged along with computer software.

*Expansion of sports exchanges, including regular meets in various sports and increased television coverage of sports. Annual binational games have been proposed by Washington. Moscow has expressed interest in boxing, bicycling, wrestling and chess matches, as well as exchanging experts in athletic medicine and narcotics-use controls.