Franklin, Golden and Munchak have not met with Penn State officials, a source said.
Golden is scheduled to meet with Penn State officials Saturday, according to a source, after the Friday's initial meeting was canceled due to weather.
But a Penn State source told ESPN's Joe Schad that Golden agreed to speak about the opening because: "It would be coming home. There is a sense of obligation about listening about coming home to Penn State."
The source said former players are supportive of Golden because they believe he understands the Penn State community, would be a willing fundraiser and ambassador, and understands the value of balancing academics and athletics.
Golden and Munchak are Penn State alumni while Franklin is a Pennsylvania native who grew up in the Philadelphia suburb of Langhorne.
The Titans fired Munchak on Saturday after the team missed the playoffs for the fifth straight season. In three seasons since Munchak succeeded Jeff Fisher as coach in 2011, the Titans have finished 9-7, 6-10 and 7-9.
Franklin, a former offensive coordinator at Kansas State and Maryland, has brought the Commodores to bowl games in each of his three seasons at Vanderbilt.
Miami has gone 22-15 in three seasons under Golden, though the Hurricanes have improved each season.
Also Friday, interim coach Larry Johnson, Penn State's longtime defensive line coach, said he planned to apply for the permanent head coach position.
"This is a great university, and there's some great players in the locker room. And not to want to be a part of that, you're crazy," Johnson said inside Penn State's Lasch Football Building. "I think our players deserve an opportunity to move forward in a smooth transition and, hopefully, I can provide that."
Johnson was hired by Joe Paterno in 1996 and is the only remaining assistant from Paterno's tenure. He has coached seven first-team all-Americans and has long been known as a hard-nosed recruiter.
He coached alongside Golden at Penn State during the 2000 season and said he was familiar with both him and Franklin. Johnson declined to speculate whether he'd remain on staff once a new coach was in place or whether he might re-hire Ron Vanderlinden, the linebackers coach who recently left the university.
"I'm not a salesperson," he said. "I am who I am, and I'm going to let my work stand for itself."
O'Brien, who spent two years at Penn State, was introduced as the new coach of the Houston Texans on Friday.
ESPN's Joe Schad and Chris Mortensen and ESPN.com's Josh Moyer contributed to this report.