Fairfax County Supervisor Martha V. Pennino, who last year turned a room in her office into a temporary shelter for the homeless, has asked the county to fund a 50-bed shelter in Reston.

Her proposal, which would create the county's third permanent homeless shelter, may come before the county board as early as Monday. County officials have supported the proposal, but have declined to discuss the shelter's projected cost. One said only that it would cost "several hundred thousand dollars."

"We don't have the needs of downtown Washington, but it would be nonsense to think we don't have the problems of an urban environment," said Deputy County Executive Verdia L. Haywood. "I don't think there is any question that it is needed."

Pennino said the shelter may be built on a vacant, county-owned lot adjacent to the Reston regional library on Bowman Towne Drive. A spokesman for Pennino said that Reston residents have been "very supportive" of Pennino's efforts to assist the homeless and that the proposal is not expected to meet any serious resistance.

The board may take up the issue Monday, when the 1987 county budget is slated to be adopted. The supervisors also will be asked to fund a 50-bed shelter on Rte. 1 near Fort Belvoir in southeastern Fairfax County. The county is being asked to pay at least $700,000 of the estimated cost of $1 million, with the Army to fund the remainder.

A $600,000 shelter in the Baileys Crossroads area is expected to open next fall. It will be located near the site of a temporary county shelter on Columbia Pike, which is scheduled to open this month.