The United Mine Workers Union has received several offers for its 75 per cent ownership of National Bank of Washington the city's third largest and oldest bank.

Bank chairman Donald D. Notman, in a separate development yesterday, said his directors have recommented a 10 per cent stock dividend through an increase in capital stock of NBW.

Union secretary-treasurer Harry Patrick, who favors selling the union's interest in the bank, said that one bid from an unidentified Arab suitor was for $50 million - "in the neighborhood" for what the UMW could consider. Reportedly, a Spanish investment organization also has expressed an interest in NBW.

Patrick is challenging incumbent union president Arnold Miller in an election campaign and informed sources said most members of the union executive committee oppose NBW, From D6> selling the stock in NBW, carried on the union's books as an asset worth $33.1 million. The bank provided the union with profits of $2.9 million in 1975 but the union has been operating with a growing deficit - $3.6 million in 1975 and $4.1 million last year.

Bank chairman Notman said yesterday overall profits lose last year and that stockholders will be asked at the March 15 annual meeting to increase capital stock outstanding to $11 million from $10 million. The proposed dividend would be distributed about April 15 if the new stock is approved by stockholders and the Comptroller of the Currency.

NBW previously paid stock dividends of 5 per cent each in 1964 and 1965 and 11.5658 per cent in 1967. In 1976, Notman said, NBW profits rose 16 per cent to $4.33 million ($4.33 a share) vs. $3.74 million ($3.74) the previous years. Not counting securities transactions for 1976, NBW earned $3.65 million ($3.65) from operations, a decline from the previous year's $3.74 million ($3.74).

Assets rose nearly 14 per cent to $653 million and deposits increased 11 per cent to a record $573.8 million on Dec. 31.