The expected appointment as ambassador to Indonesia of a Washington businessman who administration officials said has a "close" and "special" relationship to Indonesian President Suharto is stirring controversy in the State Department and the U.S. diplomatic community.

Reagan administration officials said Kent B. Crane, 47, who once served as an aide to former vice president Spiro T. Agnew, is "in line" to become the new ambassador to Jakarta. Although a final decision has not yet been made, the officials said, Crane is the leading candidate.

Suharto is due to make an official visit to Washington next month and officials said the administration will probably want to have a new ambassaor at least nominated by that time. The post has been vacant for almost a year because the administration abandoned an intended nominee in another controversy over the ambassadorship earlier this year.

Crane served in the U.S. Foreign Service in the the early 1960s in Indonesia and Africa and in the U.S. Information Agency in the mid-1970s, but in the State Department, sources say, his prospective naming has caused concern among some career Foreign Service officers. White House officials also acknowledge the potential for controversy.

Inquiries among many current and former officials, diplomats and associates reveal a concern about two issues.

Six of these sources allege that Crane worked for the Central Intelligence Agency at times during his overseas assignments in government in Africa and Indonesia. Asked about this, a CIA spokesman said that as a matter of policy, the agency declines to either confirm or deny allegations of CIA affiliation. However, one former top CIA official, who knew Crane slightly during the Agnew years, said he could not recall a CIA affiliation.

There is also concern about sending Crane as ambassador to a country in which these sources allege he has business dealings--developed after leaving government -- and a personal involvement with the presidential family, including some handling of finances. The sources did not elaborate.

There are no allegations of any illegalities. But the sources said they are concerned about potential conflict of interest.

Crane has been president of Crane Group Ltd., a consulting and international investment firm in Washington, for several years.

In a telephone interview yesterday, Crane declined to discuss his activities in or out of government. He said he was not able to talk until "something more formal happens, if it does," a reference to the decision on whether he is appointed. He said a discussion now about anything would be "inappropriate" but that he would ultimately be "anxious to talk" and to give "lots of assurances."

The post of American ambassador to Indonesia, a Southeast Asian island nation of some 150 million people, has been vacant since last November. Earlier this year it became the focus of a mysterious and extraordinary diplomatic episode. There is, therefore, also concern among some officials that a second controversy surrounding the appointment of an ambassador to the strategically important country would involve another diplomatic setback.

In the earlier episode, it was publicly disclosed that last fall President Reagan had offered the job of ambassador to a veteran diplomat, Morton I. Abramowitz, who had been ambassador to Thailand. But on May 20, a statement issued in the name of then-Secretary of State Alexander M. Haig Jr. announced with regret that Indonesia would not accept Abramowitz.

The Indonesian foreign minister later denied that his government had refused to accept Abramowitz and indicated that the issue was an internal problem of the Reagan administration.

In a detailed account of the episode, The Washington Post reported May 21 that Abramowitz had been opposed by political enemies in the administration and that an important weapon used against him was an anonymous and confidential paper, much of it inaccurate, about him that eventually found its way into the top ranks of the Indonesian government.

Although Crane declined to discuss anything about himself at this time, a biography in the 1977-1978 edition of "Who's Who in American Politics" says he worked as a third secretary in the U.S. embassy in Jakarta from 1961 to 1963 and in the State Department in 1963-1964. He is listed as then having spent time in 1964-1965 as a vice consul in the American consulate in Zanzibar, Tanzania, and as a second secretary in the embassy in Accra, Ghana, from 1965 to 1967.

After that, Crane worked on the Republican National Committee, as a special assistant to former Republican senator George Murphy, and then as an assistant for national security affairs to Agnew between 1969 and 1971.

Crane then is listed as spending 1972 to 1974 as an assistant director for East Asia and the Pacific for the U.S. Information Agency.

After that, he was an administrative assistant to Rep. Peter Frelinghuysen (R-N.J.) and, in the 1975-76 period, he served as a research director for a review of intelligence agencies for a presidential commission on the organization of government.