Rapoport mentions Morris has also received interest from two other teams.
Morris, 30, is a former sixth-round pick of the Redskins back in 2012. He played four seasons in Washington before signing a two-year, $3.5 million contract with the Cowboys in 2016 that included a $1 million base salary for the 2017 season.
Morris signed a one-year deal for the 2018 season with the 49ers in August after a rash of injuries to the position.
In 2018, Morris appeared in 11 games for the 49ers and rushed for 428 yards on 111 carries (3.9 YPC) with two touchdowns to go along with eight receptions for 73 yards receiving.