Team spokesman Charlie Dayton said Rivera was scheduled to meet with team officials in Charlotte.
The San Diego Union-Tribune reported on its website that Rivera is expected to be named the Panthers' new coach on Tuesday.
A Panthers source, however, told ESPN NFL Insider Adam Schefter in a text that the report was premature.
"Deal is he's coming in for second interview. Nothing is done. Could it happen quickly? Yes. Could it not happen quickly or at all? Yes. That is the truth."
The 49-year-old Rivera becomes the first candidate to be interviewed twice, and the first to speak directly with Panthers owner Jerry Richardson.
General manager Marty Hurney and team president Danny Morrison interviewed three other defensive coordinators last week: Perry Fewell of the New York Giants, San Francisco's Greg Manusky and Rob Ryan of Cleveland.
None of those men has received a second interview. That makes Rivera, a former linebacker with the Bears and a member of Chicago's Super Bowl-winning team in 1985, the front-runner as he seeks his first NFL head-coaching job.
A call and e-mail to Rivera's agent, Frank Bauer, weren't immediately returned.
Rivera has been with the Chargers since midway through the 2008 season. Rivera also was the Bears' defensive coordinator from 2004 to '06.
He has plenty of experience 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 Fox after his ninth season ended with an NFL-worst 2-14 record.
Richardson said last week that while he was most concerned with his team's league-worst offense, it wouldn't stop the Panthers from hiring a defensive-minded coach as long as he had a strong offensive coordinator and quarterbacks coach.
"We're putting a very high priority on the offense and that can be accomplished without having an offensive head coach," Richardson said.
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.
The Panthers have used the 4-3 scheme since Fox's arrival in 2002.
Information from The Associated Press contributed to this report.