Alexandria school officials, in response to gloomy budget projections, said yesterday they will consider saving money next year by expanding class sizes, laying off some teachers and contracting for noninstructional services.

The city School Board has requested that the staff review more than 10 savings proposals that would help them fund the 1991-1992 operating budget at its current level of about $75.7 million.

Among the measures being discussed are:

Increasing class size at elementary and secondary schools.

Eliminating nine transitional first-grade classes, which are limited to 15 students who have completed kindergarten but are not yet ready to go on to first grade.

Eliminating specialized teachers for art and music in the primary grades.

Cutting back after-school transportation and field trips.

Reducing textbook and library expenses.

Contracting cafeteria and cleaning services.

The potential cuts are in response to an anticipated reduction of $3.5 million to $4 million in state funding, according to school finance officials.

Alexandria's is the first Northern Virginia school system to publicly outline the kinds of cuts next year's budget constraints are likely to bring.

The spending crunch is further complicated, officials said, by the city government's inability to increase its proportional contribution to school costs.

Next Tuesday, the City Council is expected to consider imposing guidelines that would limit all municipal and school spending increases to 5 percent to 7 percent.

Alexandria's budget dilemma is one that a growing number of jurisdictions are coping with.

In Prince William County, where a slowing real estate market is expected to result in a $17 million revenue shortfall next year, officials announced a hiring freeze yesterday. Job interviews for prospective employees are on hold for a month while county staff members reassess their revenue projections and look for ways to save money.

Yesterday's announcement by the Alexandria School Board stems from a recent weekend retreat in Fredericksburg and sets the stage for what some city officials say is potentially acrimonious debate among council members, teachers, parents and school officials.

Council member Kerry J. Donley (D) said that school officials should look at ways to cut administrative and maintenance costs before they even consider changes that might affect instruction and teachers.

"The guidelines that we have asked the schools to live with are the same we give to the city manager to work within," Donley said. School officals said they are just trying to balance personnel costs, which make up about 80 percent of the budget, and other responsibilities.

"This may be one of those years when employees have to stand still {on pay raises} to maintain the system," School Superintendent Paul W. Masem said yesterday.

The board's position drew quick fire from a representative of the union that represents city teachers.

Alan Caudill, executive director of the 700-member Education Association of Alexandria, suggested that any attempt by the School Board to bow to the council's budget guidelines would hurt its ability to attract and retain the best teachers and would jeopardize the quality of instruction.

"The School Board is charged with forming a budget that adequately meets the needs of the system," Caudill said, adding that by cooperating, the board is allowing "the council to cop out on making the tough decisions."

Alexandria Mayor James P. Moran Jr. (D) said the School Board acted responsibly in looking at ways to save. "The reality is that the current economy is not going to allow us to fly on a first-class budget," he said.

Staff writer Brooke A. Masters contributed to this report.