As Donald Trump looks increasingly likely to be the Republican presidential nominee and looks for a running mate, one name recently surfaced and met approval from the New York billionaire. If Oklahoma Gov. Mary Fallin were chosen by Trump as his vice presidential candidate, he would be deviating from the typical strategy of choosing running mates from battleground states. Oklahoma is one of the most Republican states in the country.

That would be a good thing for Trump, South Carolina Lt. Gov. Andre Bauer, a Republican, told CNN Sunday. Trump, in turn, responded by tweeting his thanks to Bauer for the "advice," which he called "great."

Fallin was elected her state's leader in 2010 and re-elected in 2014. Previously, she was lieutenant governor for 12 years and also served two terms in the U.S. House of Representatives. Though she was re-elected with widespread support, she has been called the "country's worst governor" for botched executions, earthquakes linked to fracking and other issues. She also faces a $1.3 billion state budget hole.

While Trump and Oklahoma's governor share a number of political leanings, perhaps their chief commonality is immigration. They've both been outspoken on the topic, which came under renewed scrutiny when Trump called for a temporary ban on Muslims entering the U.S. and vowing to build a wall along the Mexican border.

Fallin, like Trump, has taken umbrage with U.S. President Barack Obama's series of executive actions announced in 2014 that would grant a path to legal status and eventual American citizenship for millions of undocumented immigrants and their children.

“President Obama’s decision to circumvent a newly elected Congress and grant amnesty to 5 million illegal immigrants undermines the rule of law,” Fallin said at the time. “The president has now unilaterally granted legal status to millions of individuals who may require state-funded medical and educational services as well as other benefits enjoyed by American citizens. All of this comes with a price tag, which the president has not addressed.”

Months before Obama's executive actions were announced, Fallin's approval ratings had been on the decline.

Another apparent similarity between Trump and Fallin is on abortion. Trump recently came under fire for suggesting there should be some type of punishment for women who get abortions. In the same vein, Fallin wants to revoke licenses from doctors who perform abortions. She could soon sign a bill into law that would characterize abortions as "unprofessional conduct" by doctors, who would then be barred from renewing their medical licenses.

Trump has not announced a short list for potential running mates, and other names have been floated around, including South Carolina Gov. Nikki Haley and New Jersey Gov. Chris Christie. Trump's son, Eric Trump, provided a list of characteristics to CNN that he said his father was looking for in a running mate.

"I think my father's been clear that he wants someone that has navigated the D.C. waterways a little more than he has to be in there," he said. That potentially leaves Fallin, who served in Congress for four years, on the short list.

Fallin, who called it a "great honor" to even be considered, downplayed the speculation. "My first and foremost goal is fulfilling my duties as governor to grow the economy while continuing to work on developing solutions for issues and challenges facing Oklahoma," she said in a statement.