Montgomery County Executive James P. Gleason said yesterday he has narrowed the possible locations for a landfill site to three, including one in the heart of the expensive Potomac-Travilah region.

The executive also announced that he is permitting the county's repeal of rent control to go into effect without his signature because he is "concerned about its effect on people with limited incomes." He urged the County Council to reconsider his proposal to increase the rent relief rebate offered to low income residents by about $100 to aid them in paying the rent increases that are expected next year.

Gleason also allowed the county's bottle deposit law to take effect without his signature. It would require residents to pay a five-cent deposit on all beverage containers. He said the law, together with the container tax levied on distributors of non-reusable containers "is adding twice the burden" on taxpayers. The container tax will go into effect JaN. 1 and the deposit law is effective Oct. 1.

Gleason said a private consulting firm will conduct an in-depth study of the three proposed trash dumping sites - at Rte. 108 and Dorsey Road in Laytonsville, Rte. 108 and Riggs Road, also Laytonsville, and Persimmon Tree Road and Bradley Boulevard in Potomac - to determine which location would provide the least hazard for residents.

The executive, however, said he is not ruling out using any of the three sites as trash dumps.

All three sites will have to be approved by the state Health Department. Earlier this month, the department ordered the county to choose a landfill site by June 1, 1978, to replace the Gude-Southlawn landfill in Rockville, which will reach its maximum capacity in 1982.

"I'm not sure this is a very happy Christmas present," Gleason said in announcing the candidates for the landfill site. After the county narrowed down the possible landfill sites to 12 in September, residents from the various communities bitterly opposed locating the site in their neighborhoods. Laytonsville residents, where five of the 12 original proposed sites are located, sent angry delegations to Gleason's office.

Potomac residents picketed one County Council meeting last month.

Informed of Gleason's decision yesterday, Potomac residents predicted his political demise and charged him with "malfeasance in office."

The proposed Potomac site sits on the 900-acre Avenel farm owned by Sheffield Enterprises, an international firm. It is adjacent to the exclusive Congressional County Club and to homes which, according to one area resident, "are valued at several hundred thousand dollars."

Most of the Potomac residents said they oppose the location of the garbage dump in their area because it would decrease their property values and threaten a setting that contains a bird refuge and "one of the purest" creeks in Montgomery County.

Gleason said he personally selected Potomac location despite the fact that "this will probably cause me a great deal of personal turmoil . . . But I could not in good conscience overlook the Potomac site."

Laytonsville residents contacted yesterday vowed that "the fight is not over" to prevent location of the facility in that area. The residents said there are at least 14 residences on the two sites under consideration, one of which is the old Riggs family homestead dating from early 19th century.

Residents there said they feared a landfill close to their homes would contaminate the well water many of them use.

Gleason also said he wants to "accelerate plans" for the county's central processing facility for recycling refuse so it can begin operating in 1981, 18 months ahead of schedule.

He said the county will begin a household newspaper collection program next year.