Beason played in 11 games with the Giants this season, picking up 65 total tackles and one interception.
He is now a free agent, but the Giants are said to be looking to bring him back for 2014.
"Jon came in and I think he stabilized our defense," GM Jerry Reese said recently. "He came in, he had a voice right away and he fit in very quickly with the players. He did a good job for us. We think it was a good trade at the time and we still think it was a good trade. We’ll evaluate Jon as we move into the offseason and we’ll see where that goes."
Beason hopes it doesn't get very far. He'd like to stay.
"I think I would love to retire as a Giant. Everyone knows how great this place is and how great it is to play for this organization, these fans, this city, this region," Beason said ofter the season. "That’s the ideal, but again, I understand that football is a business and just like the Giants are going to approach this whole situation and do what’s best for the team, I’ve got to do the same thing for myself. I have no doubt that we’ll sit down and take our time and hopefully make something happen."