Alexandria school officials, in a preliminary budget plan presented to the school board last week, have proposed a $5 million increase in school spending for the 1981-82 fiscal year. The proposal represents a 12 percent increase over the current school budget of $40 million.

Most of the proposed increase would cover hikes in teacher salaries, which represent more than 80 percent of the school budget. School officials told the board the pay hikes are needed to make Alexandria salaries competitive with those in neighboring districts.

The school board has set a public hearing on the budget plan for 8 p.m. next Wednesday at the Minnie Howard School Administration building, 3801 W. Braddock Rd. The board is expected to make a final decision on the budget Feb. 23, with city council action scheduled for May.

In presenting the budget plan last week, Superintendent Robert Peebles did not specify the exact figure for teacher pay raises, but told the board that an 8 percent hike, as suggested under city guidelines for budget increases, would be inadequate.

"It would only worsen the salary gap," Peebles contended.

Last summer Alexandria teachers and other city employes received pay increases of 10 percent, in addition to 2 percent increases for all city employes last February. Teachers also receive annual, in-step increases of 2.5 percent, which last year meant an average pay raise of 14.5 percent for most teachers.

A first-year teacher in Alexandria currently earns $12,453 a year, compared to $12,675 in Fairfax County, which has just proposed a 9.1 percent pay hike for its teachers. More senior teachers in Fairfax make higher salaries than those at the same levels in Alexandria.

The Education Association of Alexandria, which represents most of the 797 city teachers, is seeking raises of up to 13.5 percent this year. Association spokesman John C. Raiford told the school board last week that in the past five years first year teachers in Alexandria have lost "$2,411 because of inflation . . . what we're looking for is comparability, especially with Fairfax."

In addition to the salary increases, Peebles proposed eliminating 35 full-time positions, including 16 elementary and 14 secondary teachers, in anticipation of another drop in student enrollment next fall. School officials say they expect a 3 to 4 percent decline next year, or 300 to 400 students. Last fall, enrollment dropped by almost 600 to 10,838 students. In the last five years, enrollment has declined by more than 3,000 students.

The recommended reductions also include the elimination of three assistant principals, an assistant superintendent and several other administrative positions.

However, Peebles recommended the addition of eight new positions, including several preschool and special education teachers, bringing the net reduction to 22 positions. The school system currently has about 1,500 employes.

Peebles told the board some of the reductions, particularly in nonteaching posts, are part of a plan for a major reduction in administrative staff over the next several years.

Peebles said the school system also expects to propose an early-retirement program for teachers that other systems have found helps cut school budget costs.