Paterno could not be reached for comment, but he told the Pittsburgh Tribune-Review, "Sooner or later, you've got to stand for something. I feel like it's time."
In Pennsylvania, candidates for governor and lieutenant governor run in separate primaries, with the two winners in each party coming together as a ticket for the general election.
Paterno, 45, was an assistant football coach at Penn State from 1995 to 2011, when his father, Joe, was dismissed amid the Jerry Sandusky sex-abuse scandal. He and others in the late coach's family are suing to overturn sanctions the NCAA imposed on the university following the scandal, and he says in the suit that the governing body defamed him and hurt his coaching career.
A run for office would be his first.
Six other Democrats are running for lieutenant governor, including State Sen. Mike Stack of Philadelphia and former U.S. Rep. Mark Critz of Johnstown.
Wagner, 66, a Vietnam veteran, served two terms as auditor general. He ran for lieutenant governor in 2002 and governor in 2010. He was defeated in the primary for mayor of Pittsburgh last year.
The seven other candidates seeking the Democratic nomination for governor have raised more than $25 million among them. Wagner had $31,576 in his campaign fund as of Dec. 31, according to state records.
He conceded he would likely be outspent, but analysts say Wagner has one advantage: He would be the only westerner in the primary.
"His campaign would be all about geography, hoping the other candidates split up the eastern vote so he could win with a plurality," said pollster G. Terry Madonna of Franklin and Marshall College. "It's conceivable, but it's a roll of the dice."
The other Democratic candidates are York businessman Tom Wolf; U.S. Rep. Allyson Y. Schwartz and state Treasurer Rob McCord, both of Montgomery County; former state environmental secretaries Katie McGinty (Chester) and John Hanger (Dauphin); minister Max Myers (Cumberland); and Lebanon County Commissioner Jo Ellen Litz.
In statewide primaries, candidates' home counties are listed on the ballot. Solitary westerners have sometimes benefited from regional loyalties, notably in the 1978 GOP primary, when Dick Thornburgh of the Pittsburgh area defeated five other candidates for governor.
"If I were Wagner, I wouldn't make a single trip east of the Blue Mountains," Madonna said.
Former Gov. Ed Rendell, a Democrat, told reporters that unless Wagner could raise enough money for a significant TV ad campaign, "hardly anyone will hear about him."
Wagner must first gather the 2,000 signatures required to get on the ballot, including at least 100 each from 10 different counties. Paterno will need 1,000 signatures, including 100 each from five counties.
Nominating petitions are due March 11.
Inquirer staff writer Amy Worden contributed to this article.