Saudi Arabia has retained the U.S. public relations firm of a close friend and political associate of John C. West, the American ambassador to Saudi Arabia, to lobby in Washington and devise plans to improve the Saudi image in this country.

The public relations firm has just received a $65,000 contract to promote the controversial sale of 60 advanced F15 warplanes to Saudi Arabia during the next two months, and $100,000 more as the "initial payment" for a broad plan to promote Saudi-American relations in the future.

Crawford Cook, a partner in the firm who will handle the Saudi account, was West's campaign manager when he ran successfully for governor of South Carolina in 1970. Cook said yesterday he first met Saudi officials on a private visit to West in Jiddah last fall.

The decision to hire Cook to work on the proposed F15 sale represents a new, more activist posture for the Saudi government in this country. Though it has previously hired American lawyers and public relations people, this is apparently the first time it has mounted a public relations campaign here for a specific purpose of this kind.

President Carter has proposed selling the 60 F15s - this country's most advanced warplane - to the Saudis as part of a "package deal" of warplane sales to Egypt, Israel and Saudi Arabia.

Israel and the pro-Israeli lobby here oppose the package deal. The pro-Isareli lobby has already begun a concerted effort to block the F15 sale to Saudi Arabia in Congress.

Cook and about half a dozen associates in a newly opened Washington office will be urguing in favor of the F15 sale with members of Congress, reporters and anyone else who is interested.

Also lobbying for the sale will be Frederick G. Dutton, a well-connected Washinton attorney who was an associate of John F. and Robert F. Kennedy.

Dutton has been retained by the Saudi government as Washington counsel, and does a variety of jobs for the Saudis here.

They will be joined by Stephen Conner, a former vice president of Merrill Lynch Pierce Fenner & Smith in charge of international merchant banking, who is a financial and economic consultant to the Saudi government.

According to administration officials, McDonnell-Douglas Corp., manufacturer of the F15, also will lobby for the sales.

Over lunch yesterday, Cook said the pro-sale forces will offer a variety of arguments to the effect that selling the F15s to Saudi Arabia is in the best interests of the United states, and not as dangerous to Israel as the alternative, which he said would be Saudi purchases of French Mirage fighters.

Cook argued that if the F15 sale goes through, the Saudis would not be able to fly an independent squadron of the planes until 1983, and that dependence on American technicians, training, etc., would effectively deprive the Saudis of full control over the planes until the early 1990s.

But if they buy French Mirages, he contended, they would have that control much earlier. Cook said this would be more dangerous for Israel, at least theorically.

Conner will make economic arguments in favor of the sale, he said by telephone yesterday. One is that the United States must help the Saudis if they are to continue sticking to the U.S. dollar to determine the price of their oil.

Cook said the recent decline in the dollar's value and Saudis Arabia's decision not to abandon it - which has protected the United States against sharp inflation in imported oil costs - could become the best single argument in favor of the sale.

(Opponents of the sale argue that it would make Saudi Arabia an Israel terget in any future Mideast war, that it would disrupt the balance of forces in the region at a critical juncture in the search for peace, and that it would represent an implicit weaking of the U.S. relationship with Israel.)

Cook's firm is called Cook, Ruef, Spann and Weiser. Both Cook and Ruef worked for Sen. Ernest F. Hollings (D-S.C.) before setting up the firm.

They have handled a number of political campaings, either as overall campaign consultants or media advisers. Among their clients have been Sens. Walter D. Huddleston and Wendell Ford, both Kentucky Democrats, Sen. Robert Morgan (D-N.C.), and former Gov. West, now the ambassador to Saudi Arabia.

Cook described himself yesterday as a close personal friend of West's He said he was in London on business last October and decided to fly to Jiddah to visit the ambassador, at which time he happened to be included in a dinner party involving Saudi officials who were interested a public relations campaign in this country.

Cook said he made some comments on the proposals they had received from other U.S. firms, and learned later from West that the Saudi officials were interested in what he said and wanted to talk further with him. That led to his new contract to plan "a long-range cultural, educational, economic, civic and social program" to promote Saudi-American relations in the United States.

The planning alone could earn hundreds of thousands of dollars for the firm, and if the Saudis later chose Cook, Ruef to conduct the program, that might be worth millions.

Cook said his firm represents companies, including J.C. Penney, banks and financial institutions, and the South Caroline economic development board, among others. He said it would do about $7 million in business this year from offices in Charleston. S.C., and Miami.