According to Ian Rapoport of the NFL Network, head coach Matt Eberflus told reporters that Fields is day-to-day with a shoulder injury.
Fields was carted off the field after a Week 11 loss to the Atlanta Falcons and appeared to be in pain.
Rapoport said there is more optimism on Monday.
The Bears are concerned about any injury to the young man. Their development is their clearest path to becoming a contender in the near future.
Fields has become a more active player this season with his legs and his ability to make things happen. He has accounted for 832 yards and seven touchdown on the ground while completing 58.6 percent of his passes for 1,622 yards, 13 touchdown and eight interception.
It is probably best to avoid this injury if you can, given Chicago's poor record.
If Fields isn't able to play in the New York Jets game, it's likely that Siemian will get the start.
✨ Watch more top videos, highlights, and B/R original content