The report said the team is finalizing a deal to hire Mourning to work in a player development role that also will allow him to be a mentor to players both on and off the court.
His duties are yet to be defined, but he likely would work with young players, draft picks and free agents to help them adjust to the franchise and living in South Florida.
"We are in discussions with Zo and are in the stage of forming a long-term relationship," team president Pat Riley said in a statement.
Mourning, the No. 2 overall pick out of Georgetown by the Charlotte Hornets in the 1992 NBA Draft, officially retired in January after a 15-year playing career and his No. 33 was retired.
The seven-time all-star and two-time winner of the league's top defensive honor helped the Heat win the NBA title in 2006.