Speaking at a town hall in Sun Lakes, Arizona, Mitt Romney said that he would pick a running mate who "could be president" like former Vice President Dick Cheney.
Cheney, who left office with a 13 percent approval rating, has not said who he will support in 2012.
According to NBC's First Read, Romney said: "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."
"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. That's the kind of person I'd like to have, a person of wisdom and judgment."
Romney made no mention of Cheney's outspoken support of waterborading, which is defined as "torture" by international law and the Geneva Convention. Nor did Romney mention Cheney's famous claim that Guantanamo Bay was filled with "bad people," many of whom have been released due to lack of evidence.
While the former vice president didn't endorse Romney in 2008, his daughter, Liz Cheney, did join the candidate's campaign.