The Alexandria City Council voted last night to appropriate a quarter of a million dollars for a juvenile offenders' shelter if the state picks up the additional $394,000 needed.

The shelter, tentatively planned as a 14-bed modular unit to be added to the Northern Virginia Detention Home, a regional facility on South Whiting Street, is expected to be approved by the Virginia General Assembly, city officials said.

If included in the state's budget, the shelter will be built by 1987.

"We are very optimistic about it," because the state has given juvenile delinquents a high priority, said Gary Cyphers, assistant city manager for human services.

The shelter, which also may serve Arlington if that county agrees to pay a share of the capital and operating costs, would house children under 18 who are charged with or convicted of nonfelony offenses.

A recent change in Virginia law prohibits most minors charged with or convicted of misdemeanors from being held in locked facilities such as the Detention Home.

The provision, which took effect July 1, forces the City Council to spend money to house and counsel minor offenders, according to city officials.

"Some of these kids don't need to be locked behind bars," said Lillian Brooks, Director of the Court Services Unit. "What they need is a structured environment."

Mark Horowitz, the city's deputy director of social services, said the new facility would allow an offender, such as a 14-year-old convicted of petty larceny, to attend class outside the shelter while living at the shelter to receive counseling and supervision.

City Council member Robert L. Calhoun, one of the six council members voting for the appropriation of funds, said the new shelter will address the need for "something between foster care and incarceration."

In other business, the council voted last night to ask City Manager Vola T. Lawson to prepare alternate budgets for the fiscal year beginning next July. One would cut the property tax rate of $1.39 per $100 of assessed valuation by three cents and the other would maintain the present rate. The council indicated that the tax cut may be possible because new construction has increased the city's tax base.