Panthers spokesman Charlie Dayton said he couldn't confirm the move, but the team did announce that defensive coordinator Ron Meeks accepted a demotion to secondary coach.
Rob Chudzinski was hired as offensive coordinator, The Herald in Rock Hill, S.C., reported, citing two team sources.
Chudzinski, a former Cleveland Browns offensive coordinator, spent last season as the tight ends/assistant head coach in San Diego, where he worked with Rivera.
Murphy spent the last three seasons as the special teams coordinator in Minnesota, but he wasn't given any assurances by new Vikings coach Leslie Frazier when the season ended.
"Everything turned out right in the end," Murphy told the St. Paul Pioneer Press on Monday. "Everything worked out all right. It's been a great five years, and I appreciate everything from the Wilfs and Brad (Childress) and Leslie (Frazier) allowed me to do here."
The Associated Press contributed to this report