Giants general manager Jerry Reese told the newspaper Wednesday that the team "definitely will investigate it."
Burress, 32, is serving a two-year sentence for a gun possession conviction, and he likely will be disciplined by NFL Commissioner Roger Goodell for the November 2008 nightclub incident, during which the receiver accidentally shot himself while reaching for a gun inside his sweatpants. Burress played 10 games that season before the Giants suspended him. He was released by the team in April 2009.
Reese said Burress' athleticism could make an improbable comeback possible.
"When he first went in (prison) he was saying he thought he'd come back and be a good player, and I don't doubt that at all because he's that kind of athlete," Reese said. "But in this game it's hard to walk away for a couple of years and be the same person. But if anybody can do it, I think it's him. So you never say never."