The Jets have yet to address their vacancy at the top of their quarterback depth chart, but have reportedly coveted Cutler since the veteran was released Thursday.
Cutler owns 11 years of NFL experience, but his 2016 season was marred by inconsistency and injury. He underwent surgery for a torn labrum in December and was expected to be healthy by March.
The Jets voided the contract of Ryan Fitzpatrick, their 2016 starter, ahead of free agency, leaving Bryce Petty and Christian Hackenberg as the only quarterbacks on their roster. The Jets also own the sixth overall pick in this year's draft.