When he hosted "The Apprentice," Donald Trump turned an extended job interview into compelling reality TV. As the presumptive Republican nominee for president, he's taking a similar approach to picking his running mate and putting potential vice presidential candidates through a very public test. Grace Rauh filed the following report.

There's little question about who Donald Trump has been eyeing as possible running mates.

Trump is also hitting the campaign trail with vice presidential hopefuls, testing his chemistry with former House Speaker Newt Gingrich at a rally in Cincinnati.

"I'll tell you one thing, folks. I'm not saying it's Newt. But if it's Newt, no one is going to be beating him in those debates. That's for sure. Right? Nobody," Trump said.

Another strong contender for the VP spot is New Jersey Governor Chris Christie. The one-time Trump rival became an early Trump backer after dropping out of the Republican primary.

But turning what is usually a private vetting process into a very public affair does have its drawbacks. On Wednesday, two candidates for the job signaled that they are really not interested.

"I feel like I'm better suited to other kinds of things," Sen. Bob Corker of Tennessee said Wednesday.

Trump says he's been looking at 10 people to be his VP. The decision is critical, especially for a presidential candidate with no prior experience in politics or government, and even more so for one who has alienated many within his own party with his incendiary statements and tweets, including one he defended this week that was attacked for its anti-Semitic imagery.

Trump is expected to announce his running mate sometime next week. But given his unorthodox approach to campaigning, it's possible that in the end he'll surprise us all and pick someone we aren't even considering.