ESPN first reported that the Bucs and Schiano are close to an agreement.
The person spoke to The Associated Press on condition anonymity because a deal was not complete.
The 45-year-old Schiano has been with the Scarlet Knights for 11 seasons, taking them from college football laughingstock to a program that has had winning records in six of the last seven years. He was an assistant coach in the NFL with the Chicago Bears from 1996-98.
He was the University of Miami's defensive coordinator for two seasons before returning to his home state of New Jersey to coach Rutgers in 2001. Schiano is 68-67 there.
The Bucs fired Raheem Morris earlier this month after Tampa Bay went 4-12 in his third season with the team.
The timing of the move could put Rutgers in a bind with national signing day less than a week away. This is a pivotal time in the recruiting process, with coaches locking up commitments from high school prospects who make those agreements official by signing national letters of intent starting Wednesday.
Schiano's contract with Rutgers runs through 2016 and pays him around $2.35 million per year.
He played linebacker at Bucknell, but never in the NFL. His first big break in coaching came at Penn State, where Joe Paterno hired him to coach defensive backs in 1991. He was at Penn State through 1995, before being hired by the Bears.
Because of his success at Rutgers, there had often been speculation for years about Schiano possibly replacing Paterno when the Hall of Famer was done coaching. But when Penn State was looking for a replacement after firing Paterno amid a child sex-abuse scandal involving one of his former longtime assistants, the school hired Patriots offensive coordinator Bill O'Brien.
Schiano has been courted by several other colleges during his time at Rutgers, most notably Miami and Michigan.
Michigan pursued Schiano after Lloyd Carr retired in 2007. Schiano passed and the Wolverines hired Rich Rodriguez.
Schiano's first four seasons at Rutgers produced losing seasons, but the program he took over was practically at rock bottom in major college football. Before he was hired, the Scarlet Knights played in only one bowl game in their history.
Schiano brought structure and discipline to a program that sorely lacked both on every level. Not only has Rutgers become a consistent winner in the Big East, but the Scarlet Knights have regularly been among the top teams in the country when it comes to graduating players. He also helped secure funding for multimillion dollar upgrades to Rutgers' facilities, including a major stadium renovation.
In 2005, Rutgers went 7-5 and the next season the Scarlet Knights were 11-2. They have played in six bowls under Schiano, winning five, including a victory over Iowa state in the Pinstripe Bowl to cap a 9-4 season in 2011.
Follow Ralph D. Russo at www.Twitter.com/ralphDrussoAP