President Reagan has chosen William Bennett, 38, director of the National Humanities Center in North Carolina, to be chairman of the National Endowment for the Humanities, according to a variety of knowledgeable sources.

"I'm quite sure that Bennett is his choice," said one source close to the White House, "and it's just a matter of days until an announcement."

Another source in the White House said yesterday that it was "just a matter of Reagan signing the paper. I thought it might have come as early as today."

A third White House source said earlier this week that before any announcement could be made, it was a matter of "touching all the political bases."

"I don't know when an announcement is expected," said White House press officer Mort Allin. "We'll just have to wait."

Joseph Duffey, outgoing director of the endowment, told the Associated Press Bennett would be "a good choice. He's a capable administrator and an articulate spokesman."

The two most visible candidates for the job have been Bennett and Melvin Bradford, a University of Dallas, Tex., professor of English and a critic of Abraham Lincoln. Bradford has energetically and publicly campaigned for the post, noting even yesterday in a telephone interview that he claimed two more Republican senators -- Roger Jepsen (R-Iowa) and Alfonse D'Amato (R-N.Y.) -- are willing to support him. Sixteen others sent a letter of support of his candidacy to Reagan.

Bradford's main Senate supporters are John East and Jesse Helms, both Republicans from North Carolina. Their support had been formidable enough for the White House to want a cooling-off period before nominating Bennett, according to sources on the Hill and in the White House during the past few weeks.

Bradford said last night he still had no official word about who would be nominated. He denied speculation in Washington yesterday that he had been offered some other role related to the humanities instead of the chairmanship of the NEH.

"I'm not interested in concessions, that's all I'll say," said Bradford. "If the president nominates Mr. Bennett, he'll have my support."