The worldwide news agency, citing people familiar with the situation, reports that team founder Jerry Richardson has agreed to the sale, with the deal subject to a routine vote at the National Football League owners' meeting next week in Atlanta.
According to reports, the sale would be worth $2.2 billion and Tepper is reportedly keen to keep the team in Charlotte.
Tepper, 60, is the founder of Appaloosa Management and a minority owner of the Pittsburgh Steelers.
As for the Panthers, they are expected to stay in Charlotte.
There are dozens of questions regarding Tepper and what he plans to do with his new team.
The deal is expected to become final later this month with Tepper paying a reported $2.2 billion.
Forbes listed Tepper's net worth at US$11.4 billion in February of 2017. That decision came after a report by Sports Illustrated detailing Richardson's alleged misconduct. His interest in the Steelers would have to be sold before purchasing the Panthers.
The league's investigation into the allegations is still ongoing. Fixing the brand might take time, but he'll insist the franchise clean up its act immediately. He earned an MBA from Carnegie Mellon University, although it had a different name when he was attending - it's been called the Tepper School of Business ever since the magnate donated $55m to the school in 2004.
Richardson spent just $140 million for the rights to the Panthers in 1993. The Steelers have won more Super Bowls than any other team and haven't had a losing season since 2003.