Lynne Cheney, a senior editor at The Washingtonian magazine and wife of Rep. Richard Cheney (R-Wyo.), has been nominated by the Reagan administration to become chairman of the National Endowment for the Humanities, the White House announced yesterday.

Cheney, 44, who received formal notice of the nomination yesterday, declined to discuss how she would approach her potential duties, in deference to the Senate confirmation hearings she will have to face. "I think it's presumptuous to talk about it very much" until the hearings, she said yesterday.

If confirmed, Cheney will fill a post technically vacant since William J. Bennett left the agency early last year to be secretary of education. Former assistant chairman John Agresto has been acting chairman in the interim. Late last year, the Senate Labor and Human Resources Committee rejected Peace Corps Deputy Director Edward Curran for the post amid heated academic questioning of Curran's scholarly credentials.

Cheney is no stranger to Washington politics. Her husband was President Ford's chief of staff, and she was appointed last year to the Commission on the Bicentennial of the U.S. Constitution. But her connection with Rep. Cheney, she said, would be "irrelevant" to her duties as chairman of NEH, which awards grants for scholarly pursuits.

Cheney, who has a PhD in British literature from the University of Wisconsin, has also written two books -- "Executive Privilege," a White House novel written in 1978, and "Sisters," a 1981 historical thriller set in the 19th-century West -- and has coauthored a third with her husband: a 1983 history of the House of Representatives called "Kings of the Hill".

Cheney, who said she had undergone interviews with the White House for several months, still awaits the customary FBI security check, she said, which should take "about six to eight weeks." The Senate hearings probably will not take place until after Easter recess, a White House official said yesterday.

"Sometime before the Senate confirmation I'll be making courtesy calls to members of the Labor and Human Resources Committee," she said.

"Just generally, I think the Endowment is a great agency that has an important mission. From everything I've heard and observed, it has a very dedicated and competent professional staff . . . I've known John Agresto and I've known Bill Bennett and met some of the people who have worked at the Endowment and I'm very impressed with them."

Cheney will be at the helm of an independent federal agency, which allots grants from a $132.7 million budget to educational and research projects, as well as fellowships, and general humanities and state programs. It would be, Cheney said, "a commitment of many long hours . . .

"Of course I'll be leaving The Washingtonian if I'm confirmed by the Senate."