Schiano said he had not been contacted by Nebraska and declined further comment. Kelly also declined to comment.
Cincinnati associate athletic director for communications Kelby Siler told the Journal Star that Kelly wouldn't discuss rumors.
"He doesn't want to talk about it," Siler told the newspaper. "He doesn't want to field questions. We're just trying to figure out if we're going to El Paso, Charlotte or Birmingham [for bowl games] right now."
Siler told the Journal Star that athletic director Mike Thomas won't say whether he's been contacted by schools seeking permission to speak with Kelly.
Petersen, Johnson and Leavitt did not return messages left at their offices and through their schools' sports information departments.
Whoever the coach is, Osborne envisions a return to the days when Nebraska teams played a bruising brand of football and cultivated many of their best players from within the state.
Callahan junked Osborne and Solich's triple-option for the West Coast offense, and the Huskers seemed to lose their hard edge. Under Osborne and Solich, some of the most ferocious hitting occurred on the practice field. Under Callahan, practices in full pads were uncommon.
Osborne said he also wants the new coach to embrace the atmosphere, which means showing respect for the program's past, being visible and building the trust of fans and players.
"You want somebody whose word is good," Osborne said. "It's very important in recruiting that the players trust you. That what you tell them is going to happen.
"You want somebody that knows football and has a good work ethic. You want somebody that can motivate. Some people know football, but they really don't get people to play hard for them. Again, I'm not saying that's the case [with the previous staff]. But you've got to get players to play hard."
Osborne said he won't mandate a particular style of offense, but he said some facets of the old triple-option remain effective.
"I think it's really hard in college football if you don't have some mobility in your quarterback, to be successful," he said. "You need to have the ability to run the football once in a while and scramble for a first down. The rest of it, I don't know. The new coach will have to decide."
Information from The Associated Press was used in this report.