The Jets hired quarterback coach Jeremy Bates Wednesday. Bates was Cutler's quarterback coach with the Denver Broncos during his lone Pro-Bowl season.
CBS Sports' Jason La Canfora reported Wednesday that Cutler "is a possibility there at the right [price]."
Cutler signed a seven-year, $126.7 million deal in 2014 with the Chicago Bears. His pact includes $54 million guaranteed.
The 33-year-old had season-ending shoulder surgery in December. He suffered a torn labrum after passing for 1,059 yards, four touchdowns, and five interceptions.
Bears general manager Ryan Pace told ESPN last month that Cutler is "significantly ahead of schedule" in his rehab. La Canfora reported that the Bears will be "moving on" from Cutler, who will likely be released.
But the move wouldn't be a smooth transition, according to some Jets experts like the New York Daily News' Manish Mehta. Mehta wrote that Cutler's arrival "would be an unmitigated disaster."
He completed 311-of-483 passes for 3,659 yards, 21 touchdowns, and 11 interceptions in his last full season. Cutler has twice led the NFL in interceptions.