At least three prominent Republicans have been approached by White House Chief of Staff John H. Sununu about serving as chairman of the Republican Party but asked that they not be considered, sources said yesterday.

Craig L. Fuller, Bush's former chief of staff when he was vice president; Mitchell Daniels, a former White House political director, and James A. McClure, the retiring Republican senator from Idaho, all have been asked if they would be interested in being chairman of the Republican National Committee and all have said no, according to sources.

President Bush began a search for a new RNC chairman after William J. Bennett, Bush's announced choice, abruptly changed his mind last month and announced that because of financial reasons he would not accept the post. White House officials said shortly before Christmas that Bush had taken a short list of possible candidates compiled by Sununu to Camp David for the holidays to mull over a new choice. But none of the three were on the list the White House officials publicly disclosed.

Fuller, who served in the White House in President Ronald Reagan's first term and then as chief of staff to Bush in his last term as vice president, is president and chief operating officer of Hill & Knowlton's public affairs worldwide division.

Fuller could not be reached for comment, but a source said Sununu called him this week, asked if he were interested and was told no. Fuller has served as an unofficial adviser to the White House on some political and domestic issues.

Daniels, who served as a White House political director and advised the vice presidential campaign of Dan Quayle, a fellow Indiana Republican, said last night that he had not been offerred the post. Asked if he had been contacted by the White House about whether he was interested in the post, Daniels said, "No comment."

Daniels is an executive with Eli Lilly & Co., an Indianapolis pharmaceutical firm.

McClure, first elected to the Senate in 1972, retired this year. He met with Bush shortly before Christmas and sources indicated he, too, declined when asked if he were interested in the post.

Sources indicated last night that Bush had asked Sununu to "update" the list of possible candidates, which may indicate lack of presidential backing for those once thought to be front-runners, including Rich Bond, who heads a consulting firm here and who has wide backing from party professionals and several campaign officials from Bush's 1988 campaign. Bond is a former deputy chairman of the RNC, a former deputy chief of staff to Bush and was Bush's political director in the 1988 campaign.

A source familiar with White House moves on the chairmanship said Sununu is now "on a fishing expedition" in contacting a variety of possible chairmen and sounding them out for the post. "The phone lines have been pretty busy the last 24 hours," said one GOP source.

The Republican National Committee is scheduled to meet late this month to vote on the chairman. One White House official said last night that Bush would "certainly" have a candidate by then.