Virginia National Bankshares Inc. of Norfolk and First and Merchants Corp. of Richmond have begun discussions of a possible merger that would create the largest bank holding company in the Middle Atlantic States, officials of the two companies revealed yesterday.

Spokesmen for the two banks said it is unlikely that an agreement would be reached soon. Any merger would have to be approved by both bank holding companies' directors and shareholders and by appropriate regulatory agencies, a process that could take months.

If approved, the merger would be the biggest ever involving Virginia banks. The two institutions have combined assets of more than $6 billion. Currently, the biggest banking operation in the region is Maryland National Corp. of Baltimore, with assets exceeding $4 billion.

Virginia National, with assets of $3.87 billion, is Virginia's second largest bank holding company. First & Merchants is the fifth largest, with assets totaling $2.79 billion. Virginia National has 192 offices, about 37 of them in the Washingtion suburbs; First & Merchants has 113 branches, including 29 in Northern Virginia.

Officials of the two institutions declined to comment yesterday on how a merger would affect banking in Virginia and the impact on competition of combining two of the five largest bank chains in the state.

C. Coleman McGehee, chairman of First & Merchants, said merger discussions between officials of the two institutions began about a month ago. He emphasized that a merger would create a partnership and that neither institution would be acquiring the other.

McGehee declined to say who initiated the talks or why the two companies are considering a merger. C.A. Cutchins III, chairman of Virginia National, could not be reached for comment.

In a joint statement, Cutchins and McGehee said the two banking institutions felt obligated to disclose the existence of the talks after persons in the investment community began making inquiries about the subject yesterday.

In a brief telephone interview, McGehee emphasized that both institutions are strong and that earnings results in recent years have been excellent.

If the merger takes place, the result would be advantageous to banking interests served by both companies, he added. "But we have a long way to go before tying the ribbon," McGehee said.

Virginia National reported earnings of $33.3 million ($4.48 a share) last year compared with $29.2 million ($4.06) in 1981, a gain of 10.8 percent

First & Merchants had a 45 percent increase in earnings last year. Earnings per share rose from $3.04 in 1981 to $4.41.

The two banks are among the fastest growing and most profitable in the state. Virginia National's assets increased by 20 1/2 percent last year--second only to United Virginia--while First & Merchants grew by 9 1/2 percent.

The merger talks between the two Virginia banking giants are the latest result of a change in Virginia law a few years ago that removed restrictions on bank mergers, setting the stage for a round of bank consolidation.

Virginia banks also have been encouraged to grow through merger by the ongoing deregulation of financial institutions, which someday could allow District of Columbia and Maryland banks to move into Virginia.

First & Merchants has conducted an aggressive expansion program in recent years with banking-related activities in six states. Its biggest acquisition was the take-over of National Bank of Fairfax two years ago.

Virginia National has been a leader in the development of electronic banking. Two of its subsidiaries, Cash Flow Inc. and the Mid-Atlantic Exchange, have played important roles in the formation of a regional bank product development and services network.