Rapoport also reported Rivera's extension would be the first significant move for new Panthers chief operating officer Tina Becker, who took over day-to-day operations of the franchise Dec. 18.
Becker was promoted to COO after owner Jerry Richardson said he would sell the team in the wake of allegations of workplace misconduct.
Rivera, who will turn 56 on Sunday, is 64-47-1 in seven seasons as head coach. The Panthers have been inconsistent during his tenure, with four losing seasons. But he led them to an 11-5 record in 2017, and they've made the playoffs four times in the past five years.
The Panthers finished the 2017 regular season with the same record as the New Orleans Saints in the NFC South, and the teams will meet in an NFC Wild Card Game at the Mercedes-Benz Superdome on Sunday.
Carolina ranked ninth in Football Outsiders' defense-adjusted value over average metric this season.
Look for Panthers interim general manager Marty Hurney, equipped with nearly $18 million in cap space, to ensure the talent cupboards are a little more stocked next season. Carolina needs skill-position players, and its offensive line left Newton to pick himself up far too many times this year.