The Alexandria City Council, hoping to bring in badly needed tax dollars but also regulate growth, yesterday urged that the 164-acre U.S. Army Cameron Station be sold to the private sector, rather than to another federal agency, once it is shut down in 1995.

The council unanimously approved a task force report recommending that the site be predominantly residential and recreational, with limited commercial and retail space. The report also rejected a move to relocate Alexandria Hospital there.

The fate of the 170-year-old post, which recently has been home to 4,000 workers and more than a dozen Army commands, has drawn intense interest in the city since the Defense Department recommended its closing in December 1988. The Army will decide who buys the property.

The council vote reflects a long-held city government view that the site, off Duke Street in western Alexandria, should generate some tax revenue for the city. Federal installations are not subject to local taxation.

In addition to outlining potential uses and setting limits for heights and development, the council said the proposal to relocate the private, nonprofit Alexandria Hospital would be too expensive. The task force estimated that it would cost the city $88 million over a 30-year period to purchase the site.

Hospital officials, citing a space crunch and a need to expand, had wanted the city to donate 25 acres for the relocation. "We respectfully disagree with the task force conclusions," David G. Speck, chairman of the Alexandria Health Services Corp., told the council before its vote. "The constraints that exist at our {350-bed} hospital are not going to go away."

Navy officials have expressed preliminary interest in Cameron Station as a possible site for a new 20,000-employee annex. But a federal official knowledgeable about the project said yesterday that the interest apparently is not serious.