President-elect Bush has offered the Cabinet post of agriculture secretary to Clayton Yeutter, who has been President Reagan's special trade representative the past three years, a Bush transition aide said Wednesday.

Craig Fuller, co-director of the transition office, said Bush and Yeutter "met this morning and there will be an announcement this afternoon." However, the aide declined to say specifically what post the announcement would involve.Yeutter, speaking to reporters Wednesday after an appearance before the U.S. Chamber of Commerce, sidestepped questions about a new post. "Anything on that will have to come from the Bush office," he said.

In a 1986 interview, Yeutter said he always wanted to be agriculture secretary, but he abandoned that wish when he became caught up in his role as the nation's No. 1 trade representative. Reagan named him to that post in 1985.

Another possible Cabinet member, Samuel Skinner, who is a top contender for the job of transportation secretary, has not yet met with Bush, Fuller said.

On the most controversial appointment question - who will be Bush's defense secretary - Fuller said the FBI investigation into former Sen. John Tower's background should be finished by the end of the week.

Tower, the leading contender for the post, met with C. Boyden Gray, the transition's legal counsel, to go over some of the findings of the background check, Fuller said.

Several members of Congress have suggested the long process of checking out Tower would weaken him politically if and when he is chosen. But Fuller said he thought Tower would be strengthened by the process because FBI agents have left no stone unturned.

"You have to admire Sen. Tower's willingness to go through this," Fuller said.

In another development, sources said Wyoming oil and gas executive Warren Morton was in Washington and had met with top transition officials concerning the search for an Interior Department secretary.

Morton is a former speaker of the Wyoming House of Representatives, and while his background as an oil industry executive would almost certainly spark controversy from environmental groups, he is among a handful of candidates with the backing of Western state Republican senators who met last week to discuss the subject.

Sources said others acceptable to the group include Richard Richards of Utah, a former national GOP chairman, retired House Republican Leader John Rhodes of Arizona and Rep. Barbara Vucanovich of Nevada. She appears out of the running following Bush's decision not to name any incumbent member of Congress to his Cabinet.

Skinner could not be reached for comment Tuesday, although his wife, Sue, said, "I assume he probably will be" given the transportation job. "But I don't think it's been totally confirmed with him yet," she said.

Yeutter, 58, a former Nebraska farmer, was chief executive officer of the Chicago Mercantile Exchange, and served in the Agriculture Department and as deputy trade representative in the administration of President Ford.

Skinner, 50, has served since 1984 as chairman of the Regional Transportation Authority of Northeastern Illinois, the nation's second-largest mass transportation system.