Carroll has been linked with a move to Chelsea, but now any move in January appears to be unlikely after a scan reportedly revealed the severity of the injury on Thursday.
Surgery is among the options being considered and, if the 29-year-old Carroll underwent an operation he would be out for months, rather than weeks.
Hammers boss David Moyes is likely to address the matter in his news conference on Friday ahead of Saturday's Premier League clash at home to Bournemouth.
Earlier this week, Moyes had denied that West Ham were ready to sell Carroll, who has not played since Jan. 4 against Tottenham.
"At the moment Andy has an ankle injury," Moyes said on Wednesday. "He had an injection around 10 days ago and we hope that will settle and he will be available again as soon as possible."
The news of Carroll's injury may change West Ham's plans for out-of-favour forwards Javier Hernandez and Diafra Sakho. Hernandez is a loan target for Besiktas, sources told ESPN FC earlier on Thursday.
Moyes was at Chelsea's FA Cup replay with Norwich on Wednesday night, apparently watching Belgium striker Michy Batshuayi.
Batshuayi scored Chelsea's first goal in more than five hours, but his overall performance was underwhelming as he frequently squandered possession.