The Alexandria Gazette, which calls itself America's oldest daily newspaper, has been sold by the State-Record Co. of Columbia, S.C., to a group headed by Edward Neilan.

Neilan is publisher of The Asia Mail, a monthly, which he said will move into the Gazette's offices.

Neilan also is president of The Alexandria Gazette Corp., which is purchasing the newspaper, and will be editor and publisher of the Gazette. Vice president, executive editor and general manager is Lewis A. Stearman, who has been associated with The Gazette for 39 years, recently as general manager.

The sale price was not disclosed. The announcement said the paper has a circulation of about 16,000, down from 18,900 reported by the paper three years ago.

The six-day-a-week paper was established in 1784. The Alexandria Gazette has squabbled for the title of oldest newspaper in America with the Hartford Courant, which was established in 1764 but was not a daily during its early years.

The State-Record Co., which is selling the Alexandria paper, publishes papers in Columbia, S.C., Myrtle Beach, S.C., and Gulfport, Miss., and owns television stations in South Carolina, Texas and New Mexico.

Neilan, the Gazette's new editor, is a veteran Far East correspondent for the Copley Newspapers, who started The Asia Mail in 1976. He will continue to run The Asia Mail, which says it is devoted to "American perspectives on Asia and the Pacific," and to write a weekly syndicated column for Copley News Service.