The Washington rumor mill has been in gear this year concerning vacancies in the chairmanships of those sister agencies, the National Endowment for the Humanities and the National Endowment for the Arts.

In the case of one, Humanities, the choice of a candidate at last seems at hand. And in the case of the other, the rumors are picking up steam.

The Humanities job has been open since the resignation of Ronald S. Berman at the time of President Carter's inauguration. Filling the vacancy has been vexing for President Carter, with lobbying from all directions. There was an extended weeding-out process, after which two potential nominees turned down the job. The problem now seems to be solved with the nomination, expected soon, of Joseph D. Duffey, presently the assistant secretary of state for Educational and Cultural Matters.

The rumor mill is now churning again over the Arts Endowment where the chairmanship becomes vacant in the fall. In the last eight years chairman Nancy Hanks has made it a high-prfile position, and she may be stepping down.

One report, denied yesterday by the White House, was that the arts job would go to Seattle Mayor Wes Uhlman, and that deputy chairman Michael Straight would be succeeded by Livingston Biddle, congressional liaison to Sen. Claiborne Pell (D-R.I.), a figure in arts policy of Capital Hill.

An assistant to the President said yesterday: "The President has not begun to focus on the Arts Endowment chairmanship. There is no vacany until October and I doubt that the personnel office has even begun its selection process."

Another rumor, also in Seattle, strongly denied by the White House, was that the choice for the chairmanship had been narrowed to two candidates, the mayor being one of them, according to another source.