The latest rumor in Utah congressional offices is that if George Bush is elected he will name one of two Utahns as U.S. secretary of the interior - and one of the possibilities is a Democrat.

The names mentioned are former Republican National Committee Chairman Richard Richards, a native of Ogden, and former Democratic Gov. Scott M. Matheson. Rumors at the Democratic National Convention earlier this year also had said Matheson was one of Michael Dukakis's top choices for the spot.Richards said Bush has not discussed the possibility with him, and said he has little hope that Bush would appoint him. But he said, "Maybe the congressmen are talking to people who know something I don't."

Matheson laughed when asked about the rumor and said, "The speculation mill is rampant these days."

He said no one has contacted him about the position and added it would not be appropriate for him to comment further since the presidential race has not been decided yet.

"I am a Democrat, you know," he said.

The Bush campaign has a policy against commenting on possible cabinet appointments before the election.

Rep. Howard Nielson, R-Utah, said he has heard and believes the rumor. He says its sources are solid enough that "I'm spreading the rumor too."

He added, "If George Bush wins and (current Interior Secretary Donald) Hodel decides to leave, I think Dick Richards would be an excellent secretary of the interior. He has a breadth of political experience."

He said Richards might have a good shot at the appointment because he and Bush are both former national party chairmen. "There's traditionally been a strong camaraderie among that group (of former chairmen)." Richards is also working with the Bush-Quayle Campaign, helping to organize its efforts.

Nielson added that he might also support Matheson for the spot, even though he is a Democrat, to help ensure the job is held by someone familiar with the concerns of Western states.

"Scott Matheson, a popular former governor, would do a good job and he would be balanced in his approach," Nielson said. "Actually, some members of the delegation suggested him for the job when (former Interior Secretary) James Watt resigned."

Several workers in Utah congressional offices said they felt it would be politically impossible for Bush to appoint a Democrat. Richards agreed, saying, "I know George has a lot of friends who could do the job without him needing to appoint a Democrat."

But Nielson said presidents in the past have appointed people of opposing parties to their cabinets or high posts with success.

Other Utah congressmen either said they had not heard the rumor, although some on their staffs said they had, or simply had no comment about it.

Sen. Orrin Hatch, R-Utah, said he had not heard the rumor, but also said he thought Richards would be a good choice if the rumor were true.

Richards told the Deseret News: "I've had no conversation at all with the vice president about this; I'd tell you if I had. The offer is unlikely. Right now, I'm just out to help George win the election."

He added that President Reagan already once offered him the job of undersecretary at the Department of Interior under Watt when Richards resigned as national Republican chairman in 1982.

"I told him I had to leave and make some money because I had spent the last six years as a volunteer." Richards, besides being a past national chairman, has also been the state party chairman; an assistant to former Rep. Laurence Burton, R-Utah; an unsuccessful candidate for Congress against Gunn McKay in 1970; an aide in the Nixon White House; and a regional campaign director for Nixon and Reagan.

Matheson said at the Democratic National Convention in Atlanta earlier this year that he is interested in becoming the secretary of interior, but at the time was talking about the appointment possibly coming from Michael Dukakis if the Democratic presidential candidate is elected.

He also showed some bipartisan appeal when the Reagan administration said it was considering him to serve as the negotiator between the federal government and the states to find a hazardous waste site and negotiate its terms.

A third Utahn also mentioned earlier in the year as a possible cabinet member if Bush wins was industrialist Jon Huntsman. Huntsman's son, responding to rumors at the Republican National Convention, confirmed that Bush had talked to the elder Huntsman about possibly becoming the secretary of commerce. Huntsman later said he was not interested in the job.