Freeman visited the team on Monday. He also met with the Philadelphia Eagles after the 2020 campaign began.
Though his workload will probably be limited at first, the 28-year-old is likely to carve out a lead-back role with the Giants. Only Dion Lewis and Wayne Gallman are on New York's depth chart at the position.
Freeman spent the first six seasons of his career with the Atlanta Falcons before being released earlier this year. He recorded 5,987 yards from scrimmage and scored 32 touchdowns in Atlanta, earning two Pro Bowl nods.
Barkley was placed on injured reserve Tuesday.