Per Armando Salguero of the Miami Herald, Cutler is one of "multiple veteran quarterback options" the Dolphins have contacted.
Tannehill injured his knee on a non-contact play during Thursday's practice at training camp. ESPN's Adam Schefter reported there is concern within the Dolphins organization that Tannehill could require season-ending knee surgery.
Cutler does have a connection with Dolphins head coach Adam Gase, who was the Chicago Bears' offensive coordinator in 2015.
Under Gase's watch, Cutler had one of his best seasons in the NFL. The former first-round pick threw for 3,659 yards with a completion percentage of 64.4 and 21 touchdowns in 15 games. His interception percentage of 2.3 was the second-lowest mark of his career.
Cutler retired from the NFL after 11 seasons with the Bears and Denver Broncos in May. The 34-year-old immediately took a broadcasting job with Fox Sports to call NFL games this season.