A task force appointed by Prince George's County Executive Lawrence Hogan has recommended that the county build a jail at a site endorsed by Hogan -- and rejected by the County Council -- last year.

The task force on jail overcrowding, headed by District Court Administrative Judge Graydon S. McKee, recommended that the county build a new facility on the 160-acre Dille Farm Tract, a county-owned site off Brown Station Road just over a mile from Upper Marlboro. In a letter to Hogan and Council Chairman Gerard McDonough, McKee called the selection "the most architecturally feasible and cost-effective site alternative."

Although the task force report buttresses Hogan's inital preference for the Dille site, he needs council approval to build the jail there.

Hogan declined to say yesterday what action he plans on the report, which has not yet been made public. McDonough was less reticent. "The council looked at the Dille site and we definitely did not choose it for a number of reasons; the public opposition and the fact that it would require farther transportation for prisoners," he said. "As far as I know, council sentiment has not changed."

Even if the two sides were to agree on the site, the county would still have to deal with the problem of paying for the new facility. A new jail is expected to cost approximately $20 million, but Prince George's currently has only about $4 million available for the project.

The county has been struggling for years with the problem of overcrowding in the Prince George's County Detention Center in Upper Marlboro. Built to house 143 inmates in single cells, the jail now accommodates an average of 550 prisoners a day, according to jail officials, a situation that has sparked a pending class-action lawsuit on behalf of all prisoners housed there. The number of inmates is expected to reach 714 by 1990.

Last year Hogan urged the County Council to select the Dille tract over two nearby alternatives as the site for a new medium- and maximum-security facility to relieve the jail overcrowding.

In a series of contentious hearings, the council heard citizens object strongly to all three proposed sites. In October 1980 it rejected the Dille site and, after a four-month study, recommended one of the others, a 19-acre parcel of county land adjacent to the Marlboro race track. The third possible site lies behind the courthouse, where school board offices and meeting rooms are located.

Last February Hogan appointed a task force of judges, criminal justice officials and elected representatives to study overcrowding and of possible sites for a new jail. In a year-end report completed last week, it recommended the Dille site.

Yesterday Arnett W. Gaston, director of the Department of Corrections and a task force member, urged the council to reconsider its position on the Dille location. "It gives the county the opportunity to expand and not only for this decade," he said. "The site offers more security, more natural buffers. It gives room for more programs and not just for more housing. Most importantly it gives room for horizontal rather than vertical construction, which offers more security and is more cost effective."

Gaston rejected the argument that the Dille site would require the transportation of criminals through more residential areas. He said most transportation outside the jail involves prisoners on their way to court, and these people would continue to be held in the present Upper Marlboro facility.