Team owner John Mara said on ESPN 1050 Monday that the team would discuss retaining Burress' services.
"I think that's certainly something that we're going to talk about and have talked about, and I know there will be a conversation with him at some point, but where that goes I don't know," Mara said.
Then in November 2008, a handgun that Burress brought into a New York nightclub accidentally went off, shooting the wide receiver in the leg. He served nearly two years in prison on a gun charge -- New York City has some of the strictest gun laws in the nation -- and was released in June of this year.
Burress has been the subject of widespread rumors about which team will ultimately sign him this season, but most observers have not included the Giants in the mix.
Mara's interview Monday focused mostly on the just-concluded labor deal.
The Giants owner said there did come a time when he worried about the possibility that the protracted dispute might result in the cancellation of regular-season games.
"As is often the case in labor negotiations, you don't really make progress until both sides feel the pressure of the calendar, and I think that was certainly true in this case," he said.
Mara also gave a blunt response when asked why the Oakland Raiders abstained from voting on the owners' labor proposal last Thursday (they were the only NFL team that didn't vote yes on the proposal).