Norton, whom Owens has encouraged to run to succeed him, issued a brief statement announcing she would not be a candidate, but did not elaborate, the Denver Post said Tuesday.
"No question, she would have been a formidable candidate and a very good governor," Owens communications chief Sean Duffy said. "But in order to run for governor, you need to be willing to wake up every morning and devote your life to it for a year or two. And, for whatever reason, that's not in her heart to do at this point."
Norton's decision leaves state Treasurer Mike Coffman atop the field of potential GOP candidates for 2006, when Owens must leave office because of term limits.
Other Republicans who may be considering gubernatorial bids include former Denver Broncos quarterback John Elway, University of Denver President Marc Holtzman, and beer baron Pete Coors, who lost a U.S. Senate bid last year.
Democrats looking at the race include U.S. Rep. Mark Udall and Denver's Bighorn Center for Public Policy founder Rutt Bridges.