Rapoport added Raiders head coach Jon Gruden "is hoping to add him to the RB room."
Crowell carried the ball 143 times for 685 yards and six touchdowns in 13 games for New York last season. He also caught 21 passes for 152 yards.
Over his five-year career, Crowell has been a steady backfield presence who averages 4.3 yards per carry and 49.4 yards per game.
The 26-year-old would be an upgrade for the Raiders after their top two rushers, Marshawn Lynch and Doug Martin, hit free agency and remain unsigned. They might be asking a bit too much if they envision Crowell as the primary ball-carrier, though.
His best year came in 2016 when he ran for 952 yards and seven touchdowns with the Cleveland Browns. He finished 11th in defense-adjusted yards above replacement (DYAR) among running backs with at least 100 carries, per Football Outsiders.
Should they bring Crowell aboard, the Raiders would be smart to hedge their bets and target a running back at some point in the 2019 draft.