"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," Bauer told Jake Tapper on CNN's "State of the Union" Sunday. "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."

After the interview, Trump told Bauer he did a "great job" on the show and that he had great advice.

Trump's son, Donald Trump Jr., said earlier in the show that a vice presidential running mate would most likely be picked after the Republican national convention in mid-July.

"I think there are a lot of viable candidates out there, and I think some of them could have been people that have run against us in this," he said. "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."