United Mine Workers secretary-treasurer Harry L. Patrick yesterday said his union has received "nothing really firm" in terms of an offer for UMW's 75 per cent ownership of National Bank of Washington, the city's third largest bank.

In an interview after the bank's annual meeting of stockholders, Patrick also said the union had rejected outright -- "We wouldn't even consider it," he said -- an offer from an unidentified Arab source to buy the union's interest in the bank for a reported $50 million.

In other local bank industry developments yesterday:

John E. Summer Jr. was appointed vice chairman of the board and a director of American Security Bank. In effect, Sumter becomes the No. 3 officer of the city's second largest bank, joining chairman Carleton M. Stewart and president W. Jarvis Moody as the only management representatives on the board.

ASB also named Thomas Bellinger to the board and selected him to succeed Sumter as chairman of the bank's credit policy committee. Bellinger formerly was a top loan executive for Financial General Bankshares and a senior officer at Chase Manhattan Bank.

Patrick, a member of the National Bank board, is challenging UMW president Arnold Miller in a union election scheduled for June 14. At a union leadership meeting last January, Patrick detailed the benefits of income and "prestige" derived from bank ownership. He pointed out, in addition, shortcomings dictated by federal banking laws, under which the D.C. bank cannot conduct an active banking business -- home mortgages, auto loans, branches -- in regions where union membership is concentrated, such as West Virginia.

He said yesterday that if the union ever is disposed to selling its interest in NBW, "now would be the time," because of the bank's recent record of growth. "Before I would recommend selling, I'd feel a need to explain to the membership that we desire. . . It wouldn't take too much time," he stated.