Bank of Virginia Co. said yesterday that it intends to offer $3.5 million to buy all outstanding shares of the Bank of Vienna.

Bank of Virginia Co., which controls the state's third-largest bank, said that it will pay $31 a share for the $25-million-asset bank, which has offices in Vienna and Sterling. Bank of Virginia, with assets of more than $3 billion, has 120 offices throughout the state.

The purchase is subject to Federal Reserve Board approval.

Last June Bank of Virginia agreed to pay $31 a share for 24,243 shares of Bank of Vienna, which represents about 21.2 percent of the outstanding stock, from a group of investors that the bank would not identify.

A spokesman for the bank said the Vienna area is a desirable one for the Richmond-based bank because of its growth potential. The big bank has no offices in the Vienna area now.

He said that, after the bank was approached by the group of investors last June, "We felt it was an indication that others might be interested in selling. That's why we decided to make the tender offer" for all the shares of Bank of Vienna stock.

The Fed hasn't approved the June purchase of the 24,243 shares of Bank of Vienna stock.