The Cuban government and Cleveland entrepreneur Cyrus Eaton Jr. are close to an agreement on building a giant $200 million tourist center on an island just off Cuba's north coast.

The virtually uninhabited island, Key Sabinal, was chosen by President Fidel Castro, said Eaton, whose father was a pioneer in American business deals with Communist governments.

Key Sabinal is about 350 miles east of Havana and about the same distance southeast of Miami.

Cuba would be the sole owner of the complex, but financing of construction would be provided through the Canadian subsidiary of Tower International, the corporation headed by the younger Eaton.

The U.S. embargo on trade with Cuba, would prevent an American company from entering into such an agreement.

Since the 1959 revolution. Cuba's tourist trade has been limited for the most part to Canadians and East Europeans. The isolated location of Key Sabinal offers the opportunity to earn needed foreign exchange with little impact in Havana, which Castro has said was corrupted by American tourists before he came to power.

Castro said last month, in response to a rumor, that Cuba would never permit gambling casinos - famous in that era - to reopen.

Eaton said the tourist complex will be "one of the largest developments of its type in the world." Key Sabinal is three times larger than Cuba's best-known beach resort, Varadero, 70 miles east of Havana.

Like Varadero, the island has white sand beaches ideal for swimming and snorkeling.

Tower International has helped establish several hotels in Eastern Europe. A number of them have technical assistance agreements with Intercontinental Hotels, a Pan American Airways subsidiary.

In the Cuban case, there is to be no such technical assistance agreement. The hotels and other parts of the complex are to be designed jointly by Cuban and Canadian architects. Cuban materials and workers are to be used when possible.

Eaton said the agreement is to be signed next month, and the first 500-room hotel is scheduled to open in 1980, with three additional 500-room hotels opening in the following three years. Those hotels, and an airport for direct flights from the United States and Canada, would complete the first phase of construction now being negotiated.

The Cuban government has indicated that the tourist city eventually could offer between 15,000 and 20,000 rooms. Some foreign experts here think a goal of 5,000 would be more realistic.

Tower International, organized in 1964 by Eaton and other businessmen from Cleveland, New York and Canada, has undertaken projects in Eastern Europe ranging from nuclear power to movies.

Eaton's father, now 94, was an outspoken foe of U.S! policies of he early 1950s. and his advocacy of friendship with the Soviet Union led the late Sen. Thomas J. Dodd (D-Conn.) to ask for his prosecution.

In 1954, the Canadian-born industrialist inaugurated at his estate in Pugwash, Nova Scotia the informal discussions of world problems among scientists, scholars and public figures that became an international fixture.