Quinn was one of the few bright spots last season for the injury-plagued Heat, averaging 14.4 points and 5.9 assists in the final 17 games.
Quinn originally signed with Miami as a free agent in July 2006.
The Heat have been looking to upgrade at point guard this summer. Jason Williams signed with the Los Angeles Clippers in August, leaving Quinn, rookie Mario Chalmers and Marcus Banks to contend for the job.
In two years with the Heat, Quinn has averaged 5.9 points and 2.4 assists. He has played in 102 games and started 26 times.