President Carter met for 10 minutes yesterday with a sixth contender for FBI director, John A. Mintz, the FBI's chief counsel.

Mintz was not among the five candidates proposed to Carter by a nine-member committee he appointed last February to find a new director.

However, Mintz, 41, has been pushed for the job by Clarence M. Kelley, who retires as FBI director at the end of this year, and he is a favorite of other high-ranking officials.

In addition, Mintz was among several contenders mentioned to Carter by Irving S. Shapiro, the Du Pont Co. executive who heads the search committee.

In arriving at its decision, the search committee reviewed 250 names and interviewed 50 individuals. Mintz was among the top eight contenders but was not among the five names eventually forwarded to Carter. Each of those five has been interviewed by Carter for up to 17 minutes, according to a White House spokesman.

Mintz is portrayed by those who know him as scholarly and unflappable and not known to question FBI policies or practices.

A congressional aide who has dealt closely with Mintz and other FBI officials said, "I don't think Mintz would shake things up much. Mintz was legal counsel, and he was the only one who conceivably could have gotten to Kelley and said you should know what is really going on."

"He's well-spoken, competent, and has a good legal background," said a former FBI agent who is a Justice Department attorney. "He is well-regarded in the bureau."

At Kelley's request, Mintz was one of three FBI officials who reviewed an internal FBI report on allegations concerning the possibility that U.S. Recording Co., which supplied electronic devices to the FBI, might have been involved in kickback arrangements with one or more bureau officials.

The report was sent early in 1976 to then Attorney General Edward H. Levi, who rejected it and asked the bureau to investigate more thoroughly.

An FBI spokesman said the report answered the questions that had precipitated the U.S. Recording inquiry. Mintz did not return a reporter's telephone call yesterday.

Neil J. Welch who heads the FBI's Philadelphia office, is the only other FBI official being considered for the directorship, Welch, one of the five recommended by the search committee, is described as an independent, efficient administrator whose career has not been advanced by his criticism of bureau policies.

"He had trouble with [J. Edgar] Hoover because of his independence, but he overcame it," a former high-ranking FBI official said. "He was critical of some requests made to investigate individuals because he felt they were political rather than internal security investigations."

A Justice Department attorney said Welch has attacked areas of criminal activity with teams of agents, rather than assigning specific agents to head specific cases. Since the latter method gave credit to one individual other agents tended to give half-hearted support when called upon for aid, the attorney said.

"He is rough, tough, efficient and opinionated guy," he said.

The attorney said Welch has cut down on internal security investigations in favor of organized crime, white collar, and political corruption cases. However, he said Welch does not wholeheartedly cooperate with other investigative agencies.

"He'll work with prosecutors but basically believes the FBI is the greatest organization around, and the only agency that can do the job," the attorney said. "He's always been a marverick, and the bureaucrats in Washington, don't like it."