The Alexandria public housing authority, running out of money and unable to get what it considers an adequate price for a valuable tract it owns next to the Braddock Road Metro stop, is now hoping to sell the land to the city.

Last January, when the Alexandria Redevelopment and Housing Authority obtained commercial zoning for the site on which the 40-year-old John Roberts Homes project stands, it hoped to sell the property for about $10 million.

Since then, however, the real estate market has sagged and office space has become a glut on the market. By this month the authority had received only a single bid, which it rejected. The Sarubin Group, headed by Baltimore developer Morton Sarubin, offered $3.6 million immediately or $5.355 million in phased payments.

Accepting that proposal "would help us for four to five years, and that's not enough," said Angus Olson, executive director of the authority.

This week, the Alexandria City Council called for an independent audit of the housing authority's records, a request Vice-Mayor James P. Moran Jr. described as a preliminary step toward purchase of the property by the city.

Moran said he had no reason to doubt the housing agency's figures, but added the city has a "responsibility to the taxpayers to ensure that the books are accurate."

During an executive session before the weekly council meeting, council members and housing authority representatives were given copies of an appraisal dated Nov. 18. It placed the current value of the John Roberts site at $5 million, only half of the amount cited in an earlier report.

Alexandria appraiser Scott C. Humphrey said in a letter to the city last week that he is "extremely cautious and concerned about the current soft market in office building demand. Throughout the entire metropolitan area there seems to be enormous vacancies with little prospect for any early substantial increase in demand."

The housing authority provides shelter for about 3,000 people in its 1,150 units of public housing, said Olson.

The housing authority has been running a deficit of $100,000 per month, said Olson. At this rate, its reserves will be gone by the end of next month.

Olson said the authority's financial problems have grown as federal housing subsidies have been cut. Housing authorities throughout the nation have similar problems.

Until the late 1960s public housing authorities broke even, and sometimes even returned money to the federal government. But in 1969 the federal government prohibited public housing agencies from charging more than 25 percent of a family's net income for rent. With all the deductions allowed, poor families' incomes often dwindled to nothing for the purposes of calculating rent, Olson said.

To make up for the drastically reduced revenues that resulted, the federal government began to pay increasingly large shares of operating subsidies to local housing agencies.

The Reagan administration reversed that trend, and this year the federal government is expected to pay only about 70 percent of the operating subsidies local public housing agencies throughout the country will need to survive. The administration has said it wants to cut the contributions to 25 percent of the need in 1983.

As a result, housing authorities everywhere are searching desperately for ways to continue to help low-income residents. Alexandria housing officials hope one source will be a trust fund created by proceeds from the sale of property.

Many of Alexandria's poor live in the John Roberts Homes and another public housing project, the George Parker Homes, built 40 years ago -- before the town began growing into a highly desirable bedroom community for affluent Washington professionals and before the rehabilitation of the historic Old Town. Now the ground on which the two major public housing projects stand has become some of the most valuable in Alexandria.

Units of the George Parker project in Old Town face new $200,000 town houses across the street. The housing authority plans to repair the 111 Parker homes, using federal rehabilitation funds. Families from the 90 homes near the Braddock Road Metro station that are to be demolished will then move to Parker.

Affluent neighbors of the George Parker project have attacked the housing authority's plans, urging that the low-income residents be moved out to make way for town house and condominium development that will enrich the city treasury with tax receipts.

In a "position paper" distributed at this week's council meeting, some of those residents said, "The 60-square block area south of King Street have enjoyed this type of development and currently provides about $10 million in real estate taxes, which is almost 18.5 percent of the city's total tax revenue from real estate." The paper was signed by the presidents of homeowners' and citizens' associations in the area.

Vice Mayor Moran said the associations have "overestimated the proceeds" and "underestimated the costs" of their proposals.

"It could be deduced from their arguments" that the civic groups would "prefer" that Alexandria's poor leave the city, he said.

The city council, however, "is committed to providing for these people because they are Alexandrians," Moran said.