Fox Sports initially reported the trade, joining ESPN.com in citing unnamed sources saying the move will send a pair of third-round draft picks to the Dolphins.
The pair played for the Broncos from 2006-08 before Cutler was dealt to the Bears as part of an April 2009 quarterback swap involving Kyle Orton.
Marshall, who last year hauled down 81 passes for 1,214 yards and six touchdowns, was sent from Denver to Miami in 2010.
The enigmatic, 6-foot-4, 230-pound, receiver set the NFL record for most receptions in a game with 21 against the Colts in 2009.
But his off-field behavior has generated negative headlines.
Marshall was diagnosed last year with borderline personality disorder.
His wife, Michi Nogami-Marshall, was arrested in April for allegedly stabbing the player in the stomach with a kitchen knife. She told police she was acting in self-defense and was not charged in the incident.