Kristin Murphy, Deseret News
FILE - U.S. Sen. Mike Lee, R-Utah, speaks to the Utah Senate at the Capitol in Salt Lake City on Thursday, Feb. 22, 2018. If President Donald Trump's pick for the U.S. Supreme Court is Sen. Mike Lee, one of two Utahns on his shortlist, it will be up to Gov. Gary Herbert to choose the state's next senator.

SALT LAKE CITY — If President Donald Trump's pick for the U.S. Supreme Court is Sen. Mike Lee, one of two Utahns on his shortlist, it will be up to Gov. Gary Herbert to name the state's next senator.

But don't look for Herbert to appoint himself.

"I probably would not," the Republican governor said Thursday during his monthly news conference on KUED Ch. 7, calling moving from leading the state to working in Washington, D.C. "maybe a step backward."

"Being governor is a very active role," Herbert said, while he's been told by senators that role would be "kind of slow-walking stuff" and not having "as much ability to cause things to happen."

The list of possible candidates to fill a Senate vacancy in Utah would likely be long, the governor said, adding he will wait to see what action the president takes before considering replacing Lee, a fellow Republican whose current term ends in 2022.

"I don't want to get the cart before the horse," he told the Deseret News later.

Lee is joined by his brother, Utah Supreme Court Justice Thomas Lee, on the shortlist Trump prepared during his 2016 presidential campaign and is using now to name a replacement for U.S. Supreme Court Justice Anthony Kennedy.

The Utah siblings — sons of the late Rex Lee, who served as U.S. solicitor general under former President Ronald Reagan and as president of Brigham Young University — are among 25 candidates on Trump's list.

Kennedy announced Wednesday he is retiring from the high court, effective July 31.

"I'm honored to even be considered for something like this," Mike Lee said during an interview Thursday on Fox News' "Fox & Friends." He said should Trump choose his brother, "it would be fantastic" because Thomas Lee is a "terrific jurist."

During the morning news program often watched by Trump, the state's junior senator recalled first watching Supreme Court proceedings with his father as a 10-year-old. He also said he has a good relationship with the president.

"He and I don't see eye-to-eye on every issue. But on the whole, I've supported his efforts to restore federalism, restore separation of powers. These are different ways of saying, 'drain the swamp,'" Mike Lee said.

Republicans hold a 51-49 majority in the Senate, which will confirm the president's nominee to the Supreme Court. Mike Lee said he understands that he could vote for himself under Senate rules.

"You're still a senator until you're no longer a senator," he said. "You're still a senator at the moment you're being considered for something like that."

But if it's his brother who ends up being Trump's second Supreme Court nominee, Mike Lee said he'd "enjoy the opportunity to grill him as a member of the Senate Judiciary Committee."

The possibility of a Senate vacancy comes as Utah voters are set to decide in November who should replace retiring Sen. Orrin Hatch, R-Utah, after 42 years in office.

On Tuesday, Republicans chose former 2012 presidential nominee Mitt Romney over state Rep. Mike Kennedy, R-Alpine, to take on Democratic Salt Lake County Councilwoman Jenny Wilson.

Should Mike Lee leave the Senate, state law spells out that it's the governor who appoints someone to serve until the next general election, when voters would decide who should fill the remainder of the term.

In this case, the appointment would likely be until the 2020 general election, with voters electing someone to what would then be the remaining two years of Lee's second six-year term.

The law also says the governor makes the appointment from one of three names submitted by the state central committee of the same political party as the departing senator.

Herbert, however, said he has "ultimate decision-making capabilities as the governor," including rejecting names from the state GOP. But he said it's too soon to discuss how an appointment would be made in any detail.

"Let's see if, in fact, Sen. Lee gets appointed and then we can worry about it," he told the Deseret News. "We don't need to cause controversy where no controversy exists."

"It would be a big deal," said UtahPolicy.com publisher LaVarr Webb, who writes a political column for the Deseret News. He said such an appointment would be "an amazing, once-in-a-lifetime opportunity" for a politician.

Webb agreed the list of possible candidates would be a long one.

He said it could include former Rep. Jason Chaffetz, who resigned last year and is now a Fox News contributor, as well as Salt Lake Chamber President and CEO Derek Miller, who is Herbert's former chief of staff and considered a run for Hatch's seat.

Others who might be considered, Webb said, are Lt. Gov. Spencer Cox and Natalie Gochnour, an associate dean in the David Eccles School of Business and director of the Kem C. Gardner Policy Institute at the University of Utah.

Webb noted there was some talk of a Herbert run for Senate when Hatch was still making up his mind about retirement and Romney was not yet in the race. Still, he said that's not likely to happen.

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"I would discount the possibility," Webb said. "But nothing is impossible in politics."

The governor said he's ready with advice for Trump on who should be the next Supreme Court justice.

"If President Trump calls and asks for my opinion, I'm happy to give it," Herbert said. "We have two really great people here in Mike and Tom Lee, and I've proved that because I've appointed Tom Lee to the Supreme Court in Utah and he's done a great job. So he can't go wrong."