Former President Donald Trump would benefit from choosing a woman to be his vice-presidential running mate, South Dakota Gov. Kristi Noem said.
Noem, appearing Sunday on CNN's "State of the Union," said a female running mate would help the presumptive Republican presidential nominee with women voters in swing states.
"I think that that would be beneficial," Noem said. "According to the polling that I've seen for him, in a lot of swing states, is that having a woman that is helping him campaign makes a difference."
Noem, once considered a possible pick, was not among last week's reported candidates who are being vetted by the Trump campaign.
"I don't care. I love my job in South Dakota. I care about the fact that I want him to win," she said.
The only woman currently under consideration, based on recent reports, is Rep. Elise Stefanik, R-N.Y. Former South Carolina Gov. Nikki Haley, a former U.N. ambassador and former GOP presidential contender, also was not on the list.
"I've told President Trump over and over again, he needs to pick whoever helps him win," Noem told CNN. "I have been loyal to him since the very beginning when he first started to run in 2016. He's told me his priority is picking a running mate that can govern on day one."
Whatever Noem's chances of being a VP pick were, they may have suffered after the release of her recent book, "No Going Back: The Truth on What's Wrong with Politics and How We Move America Forward."
In the book, Noem recounted when she killed her pet dog named Cricket. Noem wrote Cricket proved "untrainable" after myriad attempts to keep her from being an "assassin" that was "dangerous to anyone she came in contact with."
"At that moment, I realized I had to put her down," Noem wrote.
Democrats and mainstream media outlets denounced Noem for the dog's death.
"That story's a 20-year-old story of a mom who made a very difficult decision to protect her children from a vicious animal that was attacking livestock and killing livestock and attacking people," Noem told CNN. "So it's in the book because it was difficult for me."
The Associated Press contributed to this story.