Over the past weekend, there was a report that the Falcons had Trindon Holliday in for a visit. He was not signed to a contract and agreed to a one-year deal with the New York Giants.
Hester, 31, who played at the University of Miami, had 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.
Hester, 5-foot-11. 190 pounds, was originally selected by the Chicago Bears in the second round (57th overall) of the 2006 NFL draft.
He appeared in 123 games, including 46 starts at wide receiver in eight seasons with the Bears.
Hester is one of the most prolific return men in NFL history.
He has totaled 3,241 yards on 264 punt returns and his 12.3 yards per return ranks fifth in the NFL history. Hester has also added 5,504 yards and five touchdowns on 222 career kickoff returns.
Hester, a three-time Pro Bowler, tied the NFL record for return touchdowns in 2013 recording his 19th career return score. Hester has scored touchdowns on 13 punt returns, five kickoff returns and one missed field goal return.
Last season, he led the NFL in total return yards with 1,692 and kickoff return yards with 1,436.
Hester was named to the NFL’s All-Decade team by the Associated Press for the 2000s.
He was the first player in NFL history to return the opening kickoff of a Super Bowl for a touchdown when he returned Super Bowl XLI’s opening kick 92 yards for a score.
Hester also set an NFL record with six return touchdowns in his rookie season and is one of six players in NFL history to return two kickoffs for scores in the same game on Dec. 11, 2006.
In addition to his return resume, Hester has also posted 217 receptions for 2,807 yards with 14 touchdowns during his career.