No formal announcement has been made so far, but multiple sources tell Action News that Barron will be introduced as Penn State's next president on Monday.
The university said earlier in the day the trustees would be holding a "special meeting" in State College on Monday, then confirmed the topic was "the appointment of a president."
The university said a press conference will follow the noon meeting Monday at the Penn State Conference Center and Hotel.
Rodney Erickson has been serving as the president of Penn State since November, 2011. He has said he plans to retire by June.
Erickson replaced Graham Spanier, who was forced to resign in the wake of the Jerry Sandusky child sex abuse scandal.
Sandusky was convicted nearly two years ago of 45 counts of child sexual abuse and is pursuing appeals while serving a decades-long sentence in a state prison.
The two administrators - athletic director Tim Curley and vice president Gary Schultz, both now retired - await trial in county court in Harrisburg on charges that include perjury and obstruction. Additional counts were lodged against them in November 2012, at which time Spanier also was charged.
All three men deny the allegations, and a county judge is currently dealing with their claims that the actions of a former Penn State general counsel violated their rights and should lead to the dismissal of the charges. No trial date has been set.