Gallman, 26, visited the team earlier this week.
He led the Giants in rushing last season, becoming the lead back after Saquon Barkley tore an anterior cruciate ligament. Gallman, a 2017 fourth-round choice, ran 147 times for 682 yards and six touchdowns in 2020. He also caught 21 passes for 114 yards.
In his first three NFL seasons, Gallman ran 191 times for 762 yards and three touchdowns.