The person spoke to The Associated Press on condition of anonymity because Stokley had not signed the contract.
The Giants lost veteran Steve Smith to free agency and their interest in getting another veteran increased this week after Hakeem Nicks bruised his left knee in the season-opening loss to the Washington Redskins.
The 35-year-old Stokley had 31 catches for 354 yards last season with the Seattle Seahawks. He has played 12 NFL seasons with Baltimore, Indianapolis and Denver, winning Super Bowls with Baltimore and Indianapolis. He caught a touchdown pass in the Ravens’ win over the Giants in Super Bowl XXXV.