Murray is coming off an injury-plagued season in which he finished with 659 yards and six touchdowns on the ground along with 39 receptions for 266 yards and a score. Though he started 15 games, Murray was often limited, and he struggled with a career-low 3.6 yards per carry.
Murray also averaged 3.6 yards per carry with the Philadelphia Eagles in 2015, but he bounced back with the Titans in 2016 by rushing for 1,287 yards and nine touchdowns while catching 53 passes for 377 yards and three touchdowns en route to his third career Pro Bowl.
His best season by far was 2014 with the Dallas Cowboys, as Murray set career highs with 1,845 rushing yards, 13 touchdowns and 57 receptions for 416 yards.
There is some question about whether Murray can still be a feature back, but he could be a good fit in Miami considering the Dolphins' need. Miami traded Jay Ajayi to Philadelphia last season, which left Kenyan Drake and Damien Williams as the team's top backfield options. Williams is a free agent, so Drake is the de facto No. 1 running back.
Drake rushed for 644 yards and averaged 4.8 yards per carry last season, but he may be better as a change-of-pace and third-down player than an every-down runner.
Miami figures to get stiff competition from Seattle in the battle to sign Murray since the Seahawks had one of the NFL's worst ground games last season.
Detroit could be out of the running after it signed bruiser LeGarrette Blount to a one-year deal Friday.