The next director of the FBI is expected to be chosen from a small group of experienced federal prosecutors, with the apparent front-runners being former Assistant Attorney General Richard L. Thornburgh and New York County District Attorney Robert M. Morgenthau.

That has been learned from sources familiar with the work of the nine-member committee named by President Carter to recommend a successor to retiring Director Clarence M. Kelley.

The committee, headed by Irving, S. Shapiro, chairman of E. I. du Pont de Nemours and Co., has been ordered by Carter to recommend five names to him by June 11. The President then will choose the new director from this list.

After solicting dozens of names from legal and law enforcement circles, the committee has narrowed the field to approximately 50 candidates. It meets privately here for three days each week to interview those on the list.

Because the interview is incomplete and because the final choice is up to Carter, the sources said it is too early to say who will get the job.

However, the sources added, three is a consensus within the committee about the qualifications most needed for the task of restoring the morale and reputation scandals and relevations about abuses of its power.

As a result, the sources said, much of the current, interviewing is being done only as a courtesy or fomality. They said there is an unofficial "short list" of 25 or fewer people who are the real focus of the committee's attention.

According to the sources, the dominant view within the committee is that the new director should come from outside the FBI, be a lawyer with extensive experience in the federal criminal law and have a reputation for independence.

"The feeling is that you need someone who's at a distance from the bureau but who knows how it operates and the tricks that it's capable of," one sourse said.

"By process of elimination, that means someone who's had extensive dealings with the bureau as a U.S. attorney or from within the Justice Department's Criminal Division."

Of those candidates meeting these specifications, the sources said, the committee so far seems to have been most impressed by Thornburgh, who headed the Criminal Division from 1975 until early this year, and Morgenthau, who before becoming Manhattan district attorney served several year s at U.S. attorney for the southern district of New York.

Both names are likely to cause controversy. Thornburgh, now in private law practice in Pittsburgh, is a Republican who orginally gained prominence by prosecuting Democratic officeholders in Pennysylvania on corruption charges. Morgenthau is a former unsuccessful Democratic candidate candidate for governor of New York, and his election would likely raise charges of partisanship from Republicans.

However, the sources said, other potential candidates who meet the committee's specifications - among them former Watergate Special Prosecutor Henry S. Ruth and former Assistant Attorney General Burke Marshall - reportedly have said they don't want to be considered.

Another candidate who reportedly made a favorable impression on some committee members is Stanley Sporkin, head of the Securities and Exchange Commission's enforcement division. Some sources say, though, that Sporkin may be handicapped by a feeling in big business circles that his efforts at the SEC have been overly hostile to business.

Those candidates without a legal prosecutor background fall into three rough groups, the sources said. They listed them as judges, career officials of the FBI and persons with a back-ground in local and state law enforcement.

Although several judges' names have been mentioned, the sources said, most of the those with impressive credentials have expressed reluctance to leave the bench.

Similarly, the sources said, the FBI's current problems with public image and credibility make it virtually certain that he new director won't come from the bureau's ranks. As a courtesy, though, the FBI's associate and assistant directors, as well as the heads of some FBI field offices, have been invited to apply, and serveral have been interviewed.

From the field of local law enforcement, the sources said, several candidates have been interviewed, including Robert DiGrazia, head of the Montgomery County police and former chief of police in Boston. But, the sources added, only three police officials appear to be under serious scrutiny.

They are Patrick V. Murphy, former head of the police in Washington and New York and currently president of the Police Foundation, a Washington research organizations, Francis Looney, a deputy commissioner of the New York police force who has the backing the of the International Association of Chiefs of Police, and Wilson E. (Bud) Purdy, who currently is director of law enforcement for Dale County, Fla., and who has held a broad range of law enforcement posts including service as an FBI agent.

The list ultimately forwarded to Carter is likely to contain names from all or most of these groups, the sources said. But, they added, the committee also will make clear to the President which of the recommended names are its preferences.