The White House personnel office has narrowed to 10 the candidates for nomination as the new chairman of the new chairman of the National Endowment for the Arts.

According to search committee members, the last scheduled interview is on Saturday. The committee is expected to forward one or possibly two names to President Carter by the end of next week.

Vernon R. Alden chairman of the Massachusetts Council on the Arts and Humanities and head of the Boston Company, a large financial holding firm, confirmed yesterday that he has been asked to Washington for an interview.

Among those already interviewed by the committee are:

Peggy Cooper, founder of the Workshop for Careers in the Arts: Livingston Biddle, an aide to Sen. Claiborne Pell (D-R.I.), who has drafted legislation on the arts; Kitty Carlisle, chairman of the New York State Council on the Arts and a former "To Tell The Truth" panelist, and Gunther Schaller, president of the New England Conservatory.

The search committee - composed of White House staffers Dianna Rock. Mary Ann Tighe, Marilyn Holt, Peter Kyros and Bess Abell - conducted over 200 telephone interviews in preparation for meetings with prospective candidates. They will deliver their recommendation to presidential assistant Hamilton Jordan.

Some of the search committee's interviews were conducted at the Vice President's residence with Joan Mondale present.

The present chairman of the endownment. Nancy Hanks, announced last Tuesday at the White House that she would step down from her position on Oct. 2, when her second four year term expires. Members of the committee said yesterday that they expect the President to nominate a new chairman before Hanks' term ends.