That comes after Rep. Jason Chaffetz, R-Utah, said this week he will not seek re-election, but left open the door to run for governor in 2020. Josh Romney, son of former Republican presidential nominee Mitt Romney, also is seen as a potential candidate.
"Am I seeking re-election in 2020? Well, it's a little early to make that decision," Herbert said at his news conference.
Then he jested, "Who knows, I may run for Congress" to replace Chaffetz and he jokingly said he was irritated that his name had not been included in the long list of people seen as potential candidates to replace Chaffetz.
He also joked, "I'm going to consult with Sen. [Orrin] Hatch and see what he recommends me to do." It was unclear whether Herbert was alluding to how Hatch said during his most recent election it would be his last, then changed tunes earlier this year, or to Hatch's suggestion that he might not seek re-election if Mitt Romney would run.
More seriously, Herbert said, "The state's in a good place. I'm pleased with our success and what we're doing. I'm grateful and humble about Utah being a leader of this country today."
In the same news conference, Herbert also gave high praise to Lt. Gov. Spencer Cox and said he could be a good governor, member of Congress or U.S. senator. "That's how good he is," he said.
"Spencer Cox is doing a great job as lieutenant governor. He's an outstanding talent," Herbert said. "He is a talent no matter what he will decide to run for, whether it is Senate, Congress or whether he wants to run for governor at some future time. He hasn't talked to me about it. But I know he's a very, very capable individual."
Cox was an immediate subject of speculation to run for Chaffetz's seat, but Cox threw cold water on such talk, saying he doesn't live in the 3rd Congressional District and has no plan to run for the post.
Herbert also praised Chaffetz, possibly a challenger in three years. "He served us very well, and we appreciate the service he has rendered and will continue to render until such time" as he leaves office.
Chaffetz said Thursday he may step down before his term ends in January 2019.
At the news conference, the governor also addressed numerous other topics, including efforts to possibly repeal the new Bears Ears National Monument, offering support to the embattled Utah Transit Authority, questioning the Our Schools Now ballot initiative, and addressing medical marijuana.
• Bears Ears • Herbert said he invited the secretaries of Interior and Energy and the Environmental Protection Agency administrator to visit the state and Bears Ears.
"Those three secretaries, I think, are going to come and view Utah, and see if we can't develop a practical, common-sense, environmentally sensitive pathway forward that is kind of an 'all of the above'" plan that can protect sensitive areas and allow energy development, he said.
"Repeal is certainly on the table" for Bears Ears, as is reducing its size, Herbert said.
• UTA • Herbert offered some support to the transit agency, even though one former board member was indicted recently and others are being investigated and it escaped charges by offering to cooperate with the ongoing federal probes.
He said UTA has implemented recommendations of state audits that criticized the agency, which may have solved most problems.
"With the audit and implementation of the recommendations, I think the UTA is now in a good place," he said. " I think the openness and transparency we wanted to see is now there, and corrections have been made."
• Our Schools Now • The governor again indicated that the Our Schools Now ballot initiative drive to raise taxes for education may not be needed, even though it may now try to raise sales tax and income tax for schools.
He predicted that tax reform will come next year and will increase funds for schools. He also said the best way to raise money for schools is to have a booming economy and raising taxes could dampen that and "kill the goose that laid the golden egg."
• Medical marijuana • On 4/20 April 20 when many supporters of medical marijuana celebrate its legalization in many states, Herbert said he is satisfied with Utah's slow approach to consider legalization.
"We're in the research mode here," he said, noting he and most lawmakers want to see scientific proof about the benefits of marijuana before legalization. Utah is "taking a very measured approach."