ESPN NFL reporters Adam Schefter and Chris Mortensen reported that O'Brien, 42, had been followed for the last month by the university committee charged with finding the next coach, and that the two sides would meet this week during the Patriots' bye week in the NFL playoffs.
Meanwhile, USA Today said "only contract details need to be finalized" with the committee for O'Brien to assume the job.
Approached by reporters at Penn State's pep rally at the Cotton Bowl, acting athletic director Dave Joyner said, "There is no deal in place with anybody." O'Brien was not available for comment after New England's win over Buffalo, and Patriots coach Bill Belichick would not comment when asked about O'Brien.
O'Brien's agent, Joe Linta, told bostonherald.com Sunday night that "Any imminent contract signing or agreement [with Penn State] is just off-base."
O'Brien, who is in his fifth year with the Patriots, never has been a head coach at any level. He received plenty of attention Dec. 11 when cameras caught him arguing with quarterback Tom Brady on the sideline after an interception against Washington.
Brady called O'Brien "a great coach and friend" and added, "I don't know what's going to happen. I hope he's here for a long time, and I told him that, too."
A native of Andover, Mass., O'Brien spent 14 seasons as an assistant coach with Brown, Georgia Tech, Maryland and Duke, with four of those years as an offensive coordinator. In a strange coincidence, he is a graduate of Brown, the same school that produced veteran head coach Joe Paterno.
On Saturday, reports circulated that Bradley and Green Bay Packers assistant coach Tom Clements would be given second interviews this week by the committee.