Hester, 31, who played at the University of Miami, has also told the
South Florida Sun Sentinel that he would love to play for the Dolphins.
Hester led the league in kickoff return yardage last season and was used in a limited role as a punt returner.
Jacquizz Rodgers handled the kickoff return duties last season and Robert McClain was the main punt returner. The Falcons finished 10th in kickoff-return average (24.4 yards) and 20th in punts (8.2 yards) in 2013.
The dangerous Hester has returned 13 punts and five kickoffs for touchdowns over his career.