The Panthers are putting the "finishing touches" on the deal, according to the report which cites league sources.
Rivera has been with the Chargers since midway through the 2008 season. Rivera also was the Bears' defensive coordinator from 2004-06.
He has plenty of experiencing interviewing for head coaching jobs, with Carolina marking the ninth team to talk to him over the years.
The Panthers are looking for the fourth coach in their 16-year history after Richardson decided not to bring back John Fox after his ninth season ended with an NFL-worst 2-14 record.
The son of a U.S. Army officer, Rivera lived in Germany, Panama, Washington, Maryland and California growing up and has a diverse coaching background, working with both the 3-4 and 4-3 defensive schemes.