Donald Trump is still fighting off a challenge from Texas Senator Ted Cruz in order to win the Republican nomination outright before the convention in Cleveland this summer, but it has not stopped the rumblings about who he could pick for his running mate should he get the party’s nomination.

During an appearance on CNN‘s State of the Union program this morning, South Carolina’s Republican Lieutenant Governor Andre Bauer told viewers he has a very specific pick for Trump’s vice presidential running mate.

“I think you’re going to see something different. I think what he will do is he won’t go with the norm that you pick a battleground state and you pick somebody from that state or a rival candidate. I think he’s going to say, ‘Who can help me get the job done?’ and I think he needs some balance, and I like Mary Fallin for that reason.”

Donald Trump’s veep being a woman could stop some of the discussion around his treatment of women during this campaign, from his long-standing feud with Fox News anchor Megyn Kelly to calling former opponent Carly Fiorina just short of ugly during a debate.

Fallin, a former two-term congresswoman before running successfully to two terms as governor, would give Trump credibility with those who question his ability to work with Congress and build consensus since he has never before held elected office. He has also been dogged by suggestions during this campaign that he has been challenging during the campaign, taking digs at his opponents that some have called unpresidential.

Oklahoma Governor Mary Fallin is a former member of Congress and brings experience in government Trump needs. (Photo by Win McNamee/Getty Images)

In response to Bauer’s suggestion of Fallin for Trump’s vice president, the billionaire businessman and leader in the delegate count suggested he was open to Fallin.

With the increasingly likely nomination of former Secretary of State Hillary Clinton by the Democrats, the question of whether the Republicans would nominate a female has been floating around for a while. A story by the Washington Examiner explores the possibility of a GOP ticket flanked by a female like Fallin.

“In her second term, the 60 year-old Fallin has a well-rounded resume, including a career in the private sector before entering politics and climbing a ladder that included stops in the Oklahoma House of Representatives, Congress, and lieutenant governor. Downside: Lacks foreign policy experience and has presided over a state that is so conservative, Obama lost every county in 2008 and 2012.”

Others noted in the story include South Carolina Governor Nikki Haley, who is considerably younger than Fallin at only 43-years-old. But the big downside for Haley – who is Indian-American – is not race or her sex. Trump has chided political correctness throughout the campaign and Haley’s efforts to remove the Confederate battle flag from the state capitol grounds in Charleston, South Carolina, could pose a problem with conservative voters and delegates active in grassroots politics who have gotten Trump this far in the process. Also worth mentioning is her past support for Florida Senator Marco Rubio.

South Carolina Governor Nikki Haley has been discussed as a vice presidential nominee, though her past support of Florida Senator Marco Rubio and her insistence on removing the Confederate battle flag from South Carolina state capitol grounds could limit her chances of landing the spot. (Photo by Sean Rayford/Getty Images)

New Mexico Gov. Suzanna Martinez, who was elected governor the same year as Fallin and made history by being in one of two races that year to feature two females as the major party nominees for governor (the only other time two women topped the race for governor was in Hawaii in 2002), was also mentioned as another candidate and could be a lifeline for Trump as he tries his hardest to win Hispanic voters who may have previously been turned off by his position to build a wall between Mexico and the United States.

What do you think? Who would you choose as your running mate if you were Donald Trump?

[Featured Image by Eduardo Munoz Alvarez/Getty Images]