Carter is still in the hospital and is being evaluated by both Dolphins physicians as well as kidney specialists.
The Dolphins expect to get a word on Carter's condition in the next couple of days. Wannstedt said Monday Carter had made progress since the weekend, but also left open the possibility that Carter could be lost for the season.
"He's made improvement," Wannstedt said. "He will be fine. It's just a matter of how long."
Carter began experiencing stomach problems last week, although everyone at the time assumed it was a stomach virus. Carter was able to practice Wednesday, Thursday and Friday, although he missed the beginning of the Thursday workout.
But then Carter showed up on Saturday weighing seven pounds more than he did on Friday, and everyone knew there was a significant problem and Carter went to the hospital.
Wannstedt said the Dolphins wouldn't bring in any receivers until they get a clear picture of Carter's status.
In the meantime, James McKnight has taken over for Carter in the starting lineup and Robert Baker has become the fourth wide receiver.