Per Omar Kelly of the South Florida Sun-Sentinel, Gase also said Cutler didn't ask to be guaranteed the starting job.
Dolphins starting quarterback Ryan Tannehill suffered a left knee injury in practice Thursday, and there is growing concern that he will need to undergo season-ending surgery, according to ESPN.co.uk's Adam Schefter and Jeff Darlington.
Schefter and Darlington also reported that Cutler would be willing to delay his broadcasting career with Fox Sports to join Gase and the Dolphins if he were offered the starting job.
Cutler is familiar with Gase since Gase was the Chicago Bears' offensive coordinator in 2015. During that season, Cutler threw for 3,659 yards, 21 touchdowns and 11 interceptions.
The 2016 season was a nightmarish one for Cutler, as he was limited to five starts because of injury and finished with 1,059 yards, four touchdowns and five interceptions.
As things stand, Matt Moore is operating as the Dolphins' starter. He started the final three games of the 2016 regular season as well as Miami's playoff loss to the Pittsburgh Steelers after Tannehill went down with a knee injury.
The 34-year-old Cutler has a career record of 68-71 as a starter, has started two playoff games and is a one-time Pro Bowler.