Republican presidential candidate Mitt Romney Wednesday gave voters in Arizona some insight into what kind of vice presidential running mate he would select.

The former Massachusetts governor told a town hall in Sun Lakes, Arizona he would pick someone who "could be president" like former Vice President Dick Cheney.

"I think it was last weekend I was watching C-SPAN, and I saw Vice President Dick Cheney and he was being asked questions about a whole host of issues -- following 9/11, the affairs in various countries in the world," Romney recalled, according to NBC's First Read.

"And I listened to him speak and said whether you agree or disagree with him, this a man of wisdom and judgment, and he could have been president of the United States," he said, adding, "That's the kind of person I'd like to have -- a person of wisdom and judgment."

At the same time, Romney did not rule out picking a "tea party person" for the VP slot.

Romney has also called Cheney's 2009 criticism of President Barack Obama's national security policy "direct, well-reasoned, and convincing."

While the former vice president didn't endorse Romney in 2008, his daughter, Liz, did join the candidate's campaign.

Cheney, who left office with a 13 percent approval rating, has not said who he will support in 2012.