The Reagan administration's search for a politically and professionally acceptable nominee for director of the Federal Bureau of Investigation is proving to be as difficult and time-consuming as many of the bureau's celebrated manhunts. There are simply too few candidates possessing the necessary integrity and experience -- and suitably Republican credentials.

President Reagan has had poor luck with his first three choices, Justice Department sources told our associate Michael Binstein. Former Pennsylvania governor Richard Thornburgh turned down the job; Associate Attorney General Stephen S. Trott would prefer a federal judgeship, and D. Lowell Jensen, a former Justice official, is a federal judge and "happy in San Francisco," the sources said.

Another problem besides the reluctance of those on the high-profile GOP short list is the rarity of potential candidates who have experience in counterespionage. Catching spies has become the FBI's main preoccupation, and every sign is that the "Me Decade" of espionage-for-profit will continue to demand a large share of the bureau's time and energy.

This special requirement makes one dark horse an ideal choice for the job. He is John L. Martin, chief of the Justice Department's internal security section since 1980.

Martin is probably Washington's best-kept secret, though his exploits have been behind many cloak-and-dagger headlines in recent years. In fact, the guilty parties Martin has put behind bars -- like American traitor John Walker -- and the innocents he has helped free from prison -- like Russian dissident Natan Sharansky -- are more famous than he is. What's more, Martin likes it that way. (He tried to talk us out of writing this column.)

Martin has the requisite background: one-time G-man, lawyer, counterintelligence expert and behind-the-scenes diplomat experienced in dealing with foreign intelligence services. At 49, the 10-year FBI appointment would coincide with the peak of his professional life.

Martin is not a Republican -- but he's not a Democrat, either. Political considerations have not deterred him from pursuing targets. Martin went to the mat with Justice higher-ups in 1980 and insisted on a probe into an alleged $200,000 payment by Libya to President Jimmy Carter's brother, Billy. And Martin withstood then-Navy Secretary John F. Lehman Jr.'s demand for "no deal" with John Walker -- and won Walker's cooperation against Jerry Whitworth, who might otherwise have gone free with vital information on the spy ring.

Martin joined the FBI as a special agent in 1962. After a break for private practice, he returned to Justice and by 1975 was deputy chief of the internal security section; he turned it around dramatically.

From 1966 to 1975, only two espionage cases were successfully prosecuted. In the 12 years since, Martin has supervised the indictment of 50 individuals for espionage, and the successful prosecution of almost all who went to trial.

Martin is definitely a long shot for the FBI job. But whether he gets it or not, he'll remain a kind of national treasure: a dedicated, apolitical public servant who stays on the job knowing that he could make twice as much in the business world.