The veteran tight end has repeatedly said that he is 95% sure he will retire following the end of the 2012 campaign.
The Falcons general manager told NBC Sports Network: "Tony has done so much for us on and off the field and I don't believe, not stating that he would be lying to anyone, but I don't believe the 95%.
"I want to believe it's a lot closer to 50/50, to be honest with you, and we've had discussions. Obviously [head coach] Mike Smith has had discussions with him. We're all in a good place.
"Ultimately it's up to Tony to decide if he wants to come back and potentially catch 100 balls again. I think it's one of those situations that Tony was so effective for us down the stretch and I can't imagine that his appetite wasn't sort of whet from his contributions in the playoffs."
The 36-year-old scored eight touchdowns in the regular season for the Falcons.