Northern Virginia's two largest bank holding companies revealed yesterday that they are discussing a possible merger.

New Virginia Bancorp of Springfield said it has received a formal proposal from First Virginia Banks Inc. that may lead to a merger. Officials of neither company would disclose terms of the potential merger, saying those details are still under negotiation.

The combination of the two banks -- First Virginia with assets of approximately $1.63 billion, and New Virginia with assets of about $220 million -- would not affect First Virginia's ranking among Virginia banks. In 1979, First Virginia ranked seventh-largest, well behind the Richmond and Norfolk banking firms that dominate the state.

The merger would give the combined bank broad coverage in the affluent Northern Virginia area. First Virginia is the state's oldest holding company, with a network of 21 member banks with 170 offices. Most of those are located in the urban corridor stretching from Washington to Richmond and Norfolk.

New Virginia Bancorporation is the parent of Northern Virginia Bank. In recent years it also has acquired First City Bank of Newport News and the Bank of Warrenton.

Earlier this week, New Virginia disclosed that it had formed a special committee of its board of directors to explore possible mergers. At the time, bank officials indicated that offers were coming from more than one source. A First Virginia official would not say whether the committee was considering another offer.

In another development, Virginia National Bank, a unit of Virginia National Bankshares, said it has agreed to acquire South Boston Bank & Trust Co. of South Boston, Va. Bank officials said the transaction, in which Virginia National will buy 100,000 shares of South Boston's stock for $82.50 a share, would cost $8.250 million.

The proposed merger is subject to both regulatory and shareholder approval.

Virginia National Bank has 166 offices in Virginia, an office in Nassau and assets of $2.643 billion. South Boston has three offices and assets of $51.6 million.