Nancy Hanks, chairman of the National Endowment for the Arts for the past eight years, announced at the White House yesterday that she will step down when her second four-year term expires Oct. 2.

The $52,000-a-year post is considered the most powerful in the arts-funding establishment and next year will disseminate $114 million in grants. Hanks, 49, a skilled lobbyist and speechmaker, has seen its budget increase steadily from the $11 million outlay with which she began.

A Nixon appointee, she said she informed President Carter of her decision on Thursday, after she had been summoned to the White House to discuss the future of the arts endowment.

Asked at the White House press conference yesterday if Carter offered her a third term Hanks said it never came to that. She said that she had made a personal decision "about a year ago" not to seek another term, and interrupted the President to annonce her decision before he could raise the issue. She cited "an old Southernism that it's bad manners to let somebody offer you something you are going to turn down."

The White House had no comment on a successor yesterday.

Hanks said the President told her he plans to meet the confirmation deadline.

Press Secretary Jody Powell, who presented Hanks at his afternoon briefing was asked of the President's plans and replied, "I don't have any answers to (those questions)."

The White House staff is known to be screening potential nominees however, and a name will have to be sent to Capitol Hill soon guarantee time for Senate confirmation this fall.

If there is no confirmation by Oct. 2, the endowment's deputy chairman, Michael Straight, would serve as acting chairman.

Straight is considered a potential nominee. Also reported under consideration are Livingson L. Biddle Jr., an aide to Sen. Claiborne Pell (D-R.I.); Seattle Mayor Wes Uhlamn; Peggy Cooper, founder of Washington's workshop for Careers in the Arts; and composer-conducting Gunther Schuller, a member of the Endowment's advisory National Council on the Arts.

Hanks said her decision to withdraw had been "strengthened by the commitment of President Carter and his administration to the goals for which so many people have dedicated themselves these eight years." She said the only change she recommended to the President was to appoint someone to be at his "side who think arts and has clear reading of (the President's) vision of the arts."

Hank's won plans are to "relax and reflect for a while." She will continue to live in Washington. From her tone, it didn't sound like she was ruling out future government service.

A longtime Rockefeller aide, Hanks was staff director of a 1965 landmark study which pointed out that the increasing interest in the performing arts in the United States was creating a financial bind, that demand was rising as private financing was drying up. Corporations, foundations, city and state governments were called upon to fill in the gap.

Hanks set out to implement these proposals, using matching grants and "challenge" grants to tap new sources of arts patronage.

Hanks' style was that of a national proselytizer for the arts. She knew well how to work Capitol Hill for the endowment, converting legislators who thought of the arts as frills to support of the endowment (President Ford said he was one of the converts).

A budget expert, she made a good impression in committee sessions. And a former colleague remembers that she made it a point to send greetings on birthdays and holidays. When she was nominated in 1972, the Senate didn't even bother with hearings.

By the end of the second term, though, there were signs that the honeymoon was ending. Rep. John Brademas (D-Ind.), the major figure on cultural policy in the House, was expressing concern that the endowment was forming a national base for a bureaucratic empire, and that two terms for Hanks "were enough." Sen. Pell, whose subcommitte handles endowment matters, is backing Biddle as the next nominee.

"I remember sitting in Leonard Garment's office at the White House," says Kennedy Center Chairman Roger L. Stevens, who founded the endowment and preceded Hanks as its first chairman. "Leonard said, 'Who are we going to get to replace you?' I said, 'Why not Nancy Hanks?' 'She's a woman,' Garment replied. 'Boy, could we use a woman in that job,' I think he made that decision in five minutes."

"She's and impossible act to follow," says Garment, the clarinet-playing attorney who was Nixon's arts adviser. "The President shouldn't have let her get away. She'stwo too valuable. She built the base of legislative support for the arts endowment almost singlehandedly, and she directed its work with skill, energy amd ferocious fidelity to the principles of quality and non-partisanship."

J. Carter Brown, director of the National Gallery of Art, calls her "dazzling. Remember the old definition of genius - the capacity to take infinite pains? Nancy understood that, she worked a nonstop week. No detail was too small for her attention."

Like its budget, the details of running the endowment have burgeoned. In the past year the endowment dispensed 5,050 grants, based on the opinions of its 26-member advisory board (though the ultimate decisions are up to the chairman). The endowment also coordinated the requests of hundreds of state and community arts councils with the financial support of congress, corporations and foundations.

Michael Newton, president of the American Council for the Arts, said, "She did an extraordinary job. A few years ago, I remember, we held a conference on the deariest of subjects, the administration of state arts agencies. The participants weren't famous figures, but accountants and third-level bureaucrats. Afterwards she went around saying, 'Hi, I'm Nancy Hanks,' and introduced herself to everyone. That's the way politicians behave. No one before had done it for the arts."