Asked by host Barry Young to clarify if he was saying he might run again, McCain said: "That would not be wrong."
The New York Times's Mark Leibovich, who is in Arizona following McCain, first tweeted the news.
McCain, the 2008 GOP presidential nominee, is in his fifth term. He has never taken less than 56 percent of the vote and easily dispatched a primary challenge in 2010 from former congressman J.D. Hayworth.
If he runs again, McCain will likely find himself targeted by tea party groups.
Updated at 12:36 p.m.