The veteran tight end has said that he is almost certain that the 2012 season will be his last in the NFL.
Falcons general manager Thomas Dimitroff told ESPN: "A guy who is 36 catching 100 plus balls, it just doesn't seem like it's time for him to move on.
"Tony's a man and he's got to make his own decision. Suffice it to say that it's not going to be an easy decision for him one way or another because he knows that he still has fuel in the tank and it's very legitimate fuel in the tank."
Gonzalez scored eight touchdowns during the regular season.