Gov. Chris Sununu of New Hampshire isn’t closing any doors when it comes to a possible run for the 2024 Republican presidential nomination.

"A lot of folks are coming to me. A lot of folks want me to run. It’s definitely conversations that we’re having," Sununu told Fox News in an interview on the eve of his inauguration for a fourth two-year term.

Sununu, who’s repeatedly said he is not ruling anything out when it comes to a potential White House bid, emphasized that "my first priority is New Hampshire," but added "we’ll keep having those conversations."

The governor cruised to a comfortable double-digit re-election victory in November and broadened his national footprint in recent months through a slew of cable news and Sunday talk show interviews. He said there is no timetable for his 2024 decision and emphasized there is still a year to go before the start of the presidential nominating calendar. 

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"There’s going to be a lot of time before folks even get in the race," he said. "A lot of candidates will wait to get in. They’ll see where stuff goes. See where we are politically six months from now, or a year from now. Who knows what might happen between now and then?"

While Sununu continues to enjoy healthy approval ratings in public opinion polling, he has his share of critics. 

The governor raised eyebrows last month by running digital ads in Iowa and South Carolina, which vote first and third in the GOP’s presidential nominating calendar.

"Sununu’s focus has never been New Hampshire," longtime state Democratic Party Chair Ray Buckley said. "He has spent his entire career attempting to bolster his national profile, and he’s never had qualms about leaving Granite Staters in the dust to do it."

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And he’s also taken incoming fire from his right flank as well.

One vocal critic, former Trump presidential campaign manager and top adviser Corey Lewandowski, pointed to primary losses last year by candidates in high-profile races in New Hampshire and neighboring Massachusetts who Sununu endorsed.

"Every single one lost the primary," Lewandowski said. He argued "Chris Sununu’s standing is not strong enough in the Republican Party in New Hampshire."

But Sununu is proud of his record running New Hampshire and touted in his Fox News interview that his state is "one of the strongest states in the country … economically. Businesses are pouring in. Families are pouring in." 

He also highlighted the state’s fiscal discipline, noting "we’ve cut taxes, we have these huge surpluses." 

"The process of which we’ve gained our success can absolutely be a blueprint across the country," Sununu said in what sounded like a national stump speech. "There’s no doubt about that. One of the reasons folks ask me to travel so much and come and talk to them is they’re fascinated how I’ve been able to get this done with no sales tax, no income tax. Keep getting surpluses."

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Additionally, the governor said his trips out of New Hampshire to showcase his accomplishments will continue, emphasizing that he’ll "be traveling quite a bit" in the months to come.

Sununu comes from a family with a rich political resume. His father, John H. Sununu, is a former three-term governor who later served as White House chief of staff for President George H.W. Bush. One of his older brothers, John E. Sununu, is a former representative and senator.

Despite his political pedigree, Sununu is not known as a prolific fundraiser, which could sidetrack any White House run.

The governor acknowledged that a White House run "does take fundraising because there’s a message, there’s a product, there’s a brand to be sold there. And if you don’t have the means to do it, it’s not going to go anywhere, and that’s a waste of everybody’s time and effort."

Another knock against Sununu that could negatively impact him should he eventually launch a campaign for the Republican presidential nomination is he supports abortion rights with limits.

After the Supreme Court’s conservative majority overturned the landmark Roe v. Wade ruling and sent the combustible issue of legalized abortion back to the states, Sununu emphasized, "I don’t think it’s a driving issue on the national stage … like it was because it’s not in the hands of the Supreme Court anymore, it’s in the hands of the states. It’s not in the hands of the president."

He also argued that "Republicans aren’t single issue voters, for the most part. Some are. That’s fine. But, for the most part, as a body, Republicans aren’t single issue voters."

Another Republican governor who won re-election in November by a large margin who political prognosticators also view as a potential White House hopeful is South Dakota Gov. Kristi Noem.

"I'm focused on doing my job here in South Dakota," Noem said when asked if she’s mulling a White House run. 

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But the governor, who spoke with Fox News ahead of her inauguration Saturday to a second term, added, "I’m focused here, but I’m going to continue telling South Dakota’s stories."

Noem touted that "we kept our state open" at the height of the coronavirus pandemic in 2020. 

"We balanced our budget. I’m going to bring forward and pass the largest tax cut in South Dakota history this legislative session," she added. "We protected parental rights. We reformed our education system, and it’s working.

"Our state is thriving because we put forward and put in place conservative policies. That’s a story that I think can bring hope to the rest of the country."

Asked if she'd consider a 2024 presidential run, Noem said "that’s fair to say."

"But there are a lot of people out there talking about running for president," she added. "I also know that politics changes quickly, and things change on a dime on who’s going to run and who’s not going to run. I want the best person.

"We need a way better president than the one we’ve got today. Joe Biden’s a disaster. So, Republicans really do need to focus on getting a candidate for presidential office that can win."