The 32-year-old, who picked up the injury in Rangers' opening Premier League match against Bolton, is expected to be out of contention until Christmas.
"It's not looking good for Kieron, and it looks as if he will need a lengthy rehab," Warnock told the Fulham Chronicle.
"There seems to be new ligament problem at the front of his foot, and he has been in a lot of pain. I feel for the lad, especially after the training and effort he's made to get back."
The 62-year-old boss revealed that he would like to keep the former West Ham United player until the end of the season.
"There has been talk we would maybe think of finding Kieron another club at Christmas, bearing in mind we have a number of new players," he added.
"But I would like to keep him until the end of the season - he deserves that at least."
Dyer made the switch to the London club this summer after a loan spell at Ipswich Town.