The Alexandria City Council spent almost three hours last night interviewing 10 of the dozen people who want to be appointed to the city's School Board.

Three seats on the nine-member board will be open, and the three incumbents are all seeking reappointment by the council, which is scheduled to make its selections tonight.

Two of the incumbents, Board Chairman Lou Cook and Mary Jane Nugent, were among those interviewed separately by the council last night. The third, J. Harvey Harrison Jr., was unable to attend.

At least two of the incumbents, Cook and Nugent, are given a good chance for reappointment by sources close to the council, and a favorite for the third spot was said to be Rhonda Hill, who teaches in the Fairfax County school system. If Hill, who is black, gets the job, the number of blacks on the board would rise to three.

Last night the council interviewed Hill, homemaker Linda Burch, attorney Gene Lange, retired D.C. school teacher Dorothea Carter, former Louisville, Ky., PTA official James Harris, freelance writer Roy Gordon, former Michigan school teacher James Scott and longtime PTA member Jean Swersky.

A. Melvin Miller, an attorney who is the second black seeking School Board appointment this year, was unable to attend the interview session.

Unlike school districts in Washington and Maryland, members of local Virginia school boards are appointed by local governing bodies.