Tuck has the sixth-most sacks in Giants history, has played a key role in two of the franchise's four Super Bowl titles and is a fair bet to be enshrined some day in the team's ring of honor.
But when Tuck takes the field at MetLife Stadium on Sunday for the 2013 season finale, he won't know whether it will be his final game as a Giant.
"I'll be a little teary-eyed after I walk off the field, maybe," Tuck said Thursday. "I won't say definitely, but maybe. It makes a better story if I say teary-eyed."
Joking aside, Tuck does seem to be a man at peace about the situation. His contract expires at the end of the season, and he will be an unrestricted free agent.
Tuck turns 31 in March, and while he's had a strong overall season around his nine sacks, the two seasons that preceded this one were not great. The Giants have a difficult decision to make about whether and at what price to try to re-sign him.
Although Tuck has made it clear that he would like to be back with the Giants, he knows nothing has been decided yet -- by him or by the team.
"It's not, 'Definitely I'm going to be here,' and it's not, 'Definitely I'm not going to be here,'" Tuck said. "So I'm just focused on trying to win the game, and we'll see what happens after that."
Tuck said he has had no conversations with the Giants about a new deal. He said he told his agent and Giants general manager Jerry Reese last year that he didn't want to talk about the contract until this season was over, and they have honored that wish.
"I told them I don't want to hear about it," Tuck said. "So I honestly don't know if they've talked or not, I guess. I just know I haven't heard about it."