Reston yesterday offered Fairfax County a free site of up to 150 acres to move its cramped governmental center from Fairfax City to the new town.

The offer, which could be worth up to $7.5 million, based on current land prices, come as the county considers relocation of its seat of government. Growth of the government - paralleling the rapid development of Fairfax - quickly filled up the Massey Building headquarters when it was opened in 1970. The county since has been forced to scatter offices and employees to rented buildings near its governmental complex at 4100 Chain Bridge Rd., in Fairfax City.

Because of its location, the county not only has had to rent space - for $750,898 this fiscal year - but also loses tax revenues from a variety of county government-related commerical development; that go to Fairfax City, an independent jurisdiction.

The chairman of the county's relocation study committee, attorney Michael S. Horwatt, said Reston's offer "is certainly a factor we will have to consider. . . . It may be decisive."

However John F. Herrity, chairman of the Fairfax Board of Supervisors, said, "The first thing to be considered is whether the center should be moved.If the answer is yes, you have to ask, how accessible is the site (Reston)? How would a citizen from Mount Vernon who has county business to conduct get to Reston?"

Board Vice Chairman Martha V. Pennino (D-Centreville), whose district includes Reston, said the offer of a free site "enchances" the new town's chances of becoming the new capital. But she acknowledged that the area, in the northwest corner of the county, is in the "far reaches" of Fairfax. But she said that based on growth projections, one-fifth of the county's population will be living in the Reston-Herndon area within 10 years.

While a large new site in Reston would probably solve the ever-worsening parking problem at the Fairfax City complex, there would be other transportation problems. Reston is easily reached from the Tysons Corner area, via Rte. 7, and is divided by the Dulles Airport Access Road.

But there is no major north-south route connecting the new town with the fast-growing southern part of the county. Mount Vernon-area Residents, depending on their location, are 25 to 28 miles from Reston on a roundabout route.

Reston's offer was made James W. Todd, president of Gulf-Reston Inc., the new town's developer, in a letter to Horwatt.

While no decision has been made on relocating the county offices, there is growing sentiment for moving all or part of the governmental center out of Fairfax City.

"The Board of Supervisors feels down to the last person that a shift is overdue," Pennino said.

Horwatt, while stressing that the relocation committee has made no decision said, "The space the county now has - 40 acres - is inadequate for any meaningful expansion of facilities. That doesn't necessarily lead you to the conclusion that you move the center. But it does lead you to the conclusion that alternative sites have to be found for expansion." The committee expects to complete its report in February.

Herrity, stressing, the county is spending $750,000 annually on leased spaced in Fairfax City, said the decision on whether to relocate will be based on "economics - what the cost will be to taxpayers."

The letter from Gulf-Reston's Todd to Horwatt said a governmental center could be built in Reston in such a way that there would be "limited front-end costs (initial capital investment)" for the county. As Todd noted, Reston was able to attract the U.S. geological Survey in 1969 by donating all the land to the federal government and building the office center with revenue bonds. After leasing the building from Gulf-Reston for 20 years, the federal government will own its outright.

Reston is one of three sites that have been mentioned as potential homes for a relocated governmental center. The other two, both on the Capital Beltway, are at Tysons Corner and the Chiles tract, which extends along both Rte. 50 and Gallows Road.

The original seat of the county, founded in 1742, was at Tysons Corner, in an area called Freedom Hill, on the south side of Rte. 7. The courthouse, the center of governmental activity for many years, later was moved to Alexandria, and in 1800 was shifted to its current location in Fairfax City.

If the entire governmental complex is relocated, completion of the new courthouse, now scheduled to be built near the Massey Building in Fairfax City and ready by 1980, could be delayed for a year, county officials said. Relocation of the courthouse - but not other governmental facilities - would require a referendum.

Chief Judge Barnard F. Jennings of the Circuit Court said yesterday, "I hate to see anything cause a delay. We are desperate." Present court facilities are badly strained by the mounting caseload. Handcuffed prisoners are led past visitors, and sometimes even judges who sentenced them. Records are crammed wherever there is space. Until recently, George Washington's will was stored with confiscated Heroin and other police evidence.

A new jail has been built at the present Fairfax City complex and is scheduled to open shortly. Altogether, the county government has 5,400 employees, of which 2,125 work in the Fairfax City complex of offices, including rental facilities.

If Reston became the new county seat of Fairfax, or a secondary governmental center, its sluggish development could be greatly accelerated.