The Miami Herald and South Florida Sun-Sentinel reported Miami has passed on Dampier, who was released this month by the Charlotte Bobcats.
Dampier, 35, held a meeting with Heat President Pat Riley Wednesday at AmericanAirlines Arena, but the get-together didn't end with a contract for the 15-year veteran.
The Heat have already signed Dwyane Wade, LeBron James, Chris Bosh, Mike Miller and Udonis Haslem this off-season and had limited room remaining under the league's salary cap.
Instead of signing Dampier, the Heat will go with veterans Joel Anthony, Zydrunas Ilgauskas, Jamaal Magloire and rookie Dexter Pittman at center in training camp, the Sun-Sentinel said.
Celebrity Families of 2014 [PHOTOS]