As soon as the Senate rejected John Tower's nomination as defense secretary, two Utahns quickly emerged in rumors as possibilities to be the next nominee: Sen. Jake Garn, R-Utah, and National Security Adviser Brent Scowcroft.

Garn is generally considered a longshot for the nomination - even though his fellow Sen. Orrin Hatch, R-Utah, said Garn may now be the best man for the job.Meanwhile, Scowcroft was seen as the odds-on favorite by many, even though the Washington Post said Friday that he reportedly does not want the job. It reported, however, administration officials are still divided about whether he should take it.

One scenario in the Scowcroft rumor would even have Tower replace Scowcroft as national security adviser - because that post doesn't require Senate confirmation. Even though it is a Cabinet-level position, it is technically just a White House staff post.

Both Garn and Scowcroft are native Utahns and both are retired officers - Garn from the Air National Guard as a lieutentant colonel and Scowcroft from theAir Force as a general.

As reporters asked senators about who might be the next nominee, the names of Garn and Scowcroft came up often - as did the name of Donald Rumsfeld, a cabinet member in the Nixon administration. Garn was not mentioned as often as the other two.

Garn's reaction to the rumors was, "The Jake Garn rumor is a Jake Garn rumor. I don't know where it originated, but no one from the administration has talked to me - and I've had several opportunities on other issues to meet with them. So the only place I've heard the rumor is in the press."

He added, "I'm enjoying being in the Senate." But he said, "I probably would not turn down the opportunity (to be defense secretary), but I certainly would not expect to be asked."

But one person who said that maybe Garn should be asked was Hatch.

He told members of the national press gathered in the Senate press gallery, "There are a number of people who could do the job, not the least of whom would be my colleague Sen. Jake Garn - I think he would be very good.

"I don't think this president can afford to lose another senator. . . . But he (Garn) is a person who I think will bring about Pentagon reform. He's got the guts to do it and the brains and the ability."

Meanwhile, Garn was full of praise for Scowcroft as the possible next nominee.

"Brent would certainly be well-qualified for the position," he said. "But I obviously have a bias. I've known Brent Scowcroft for a long time. He's a Utahn. He's extremely knowledgeable and would be a good choice."

Garn is considered a "clean choice" by rumor spreaders. The clean-cut, non-drinking LDS Church member is not expected to present any of the wine, women or conflict-of-interest questions that plagued Tower.

Scowcroft has said in interviews that he drinks a little wine with his dinner. But his work as national security adviser for Presidents Ford and Bush and work on numerous commissions for Presidents Carter and Reagan have brought him a solid reputation.

He has performed work for defense contractors - which might lead some to question whether that presents a conflict of interest. Rumsfeld - the other most often mentioned in rumors - also has served as a board member for defense contractors.

Scowcroft was born in Ogden, and credits his LDS upbringing for instilling a strong work ethic - although he said he is no longer very active in the church. He is known for working 18-hour days in the White House.