Harry T. Edwards, a 38-year-old professor at the University of Michigan Law School and a specialist in labor law and arbitration, is expected to be nominated to the U.S. Court of Appeals here.

Edwards, who also is chairman of the board of directors of Amtrak, would succeed David L. Bazelon, a judge on that court for 30 years who assumed the part-time status of a senior judge last June,

Sources confirmed yesterday that the FBI and the American Bar Association are conducting background investigations on Edwards, which is the last step before President Carter submits his formal nomination to the Senate.

If his nomination is confirmed, Edwards would become the second black and one of the youngest lawyers selected for a seat on that bench. Bazelon, who was chief judge of the influential appeals court for 15 years, was 40 years old when President Truman appointed him to the court in 1949.

Edwards, in a telephone interview yesterday, said, "I'm gratified to know that I am under serious consideration for the job," but declined further comment. Neither the White House nor the Justice Department would comment on reports that Edwards is Carter's choice for the job.

Lawyers who know Edwards, described him as generally liberal, although they were reluctant to put him in a political category. One law professor commented that Edwards' professional career as an arbitrator and mediator does not lend itself to that kind of description.

The appeals court here handles a variety of labor-related cases, including petitions brought in opposition to rulings by the National Labor Relations Board. In recent years much of the court's work has focused on cases appealed from the federal regulatory agencies on claims ranging from employment discrimination to civil rights violations.

An honors graduate of the University of Michigan Law School in 1965, Edwards worked for five years at the Chicago law firm of Seyfarth, Fairweather & Geraldson, in labor and administrative law, then returned to the university to teach.

As a teacher, Edwards specializes in labor law, collective bargaining and negotiations, and law related to higher education -- issues such as freedom of expression and federal regulation of academic institutions. While he is widely regarded as a scholar in those fields, colleagues noted yesterday that Edwards has had extensive practical experience in the labor field.

Edwards has acted as a neutral arbitrator in a variety of labor disputes, including cases involving the Ford Motor Co. and the United Auto Workers, and U. S. Steel Corp. and the steelworkers union. Edwards has also been appointed by the federal court in Detroit to oversee distribution of a $5 million settlement of an employment discrimination case brought against the Detroit Edison Co.

Edwards, who left Michigan in 1975 to teach at Harvard University Law School, was described as a popular teacher who was highly regarded by his associates on the Harvard faculty. He returned in 1977 to the Michigan Law School in Ann Arbor, where he now lives with his wife, Ila, and their two young children.

Carter appointed Edwards to the Amtrak board of directors in 1977. Amtrak, the National Railroad Passenger Corporation, was established by Congress in 1970 and oversees the operation of 259 trains and 27,000 miles of railroad. Edwards was elected chairman of the board in April. His term on the board expires in July 1980.

Edwards would be President Carter's third nominee to the appeals court here, considered to be one of the most prestigious -- and powerful appellate courts in the nation.

Former assistant attorney general Patricia M. Wald was confirmed to a seat on that bench last summer, despite opposition from conservative groups that objected to some of her writings in the area of family law.

However, Carter's second nominee, Rep. Abner J. Mikva (D-Ill.), has faced stiff opposition from the National Rifle Association, which vigorously objects to Mikva's support of gun control legislation.

Mikva's nomination is expected to reach the Senate floor this week. Meanwhile, a source said yesterday, NRA members yesterday flooded senators with mailgrams and telephone calls in protest of Mikva's nomination.

The NRA has also argued that Mikva is constitutionally barred from the court appointment because he was a member of Congress when its members were voted a pay raise. In response, the Justice Department said that Mikva would not be precluded from the judgeship if his nomination is confirmed by the Senate before Oct. 1, the date the pay raise is effective.

The constitutional question has raised concern among Mikva supporters, who expect that the Senate vote on his nomination will be a close one.

Mikva and Wald were nominated to fill two new seats on the appeals court here.