"It is possible Angel will need surgery," Carvalhal said, adding that midfielder Leon Britton is also struggling with the same muscle problem.
"Leon will have an injection and he will soon be training with us, but Angel will be longer," Carvalhal added.
Sanches injured his hamstring in an FA Cup game last month while Fer (Achilles) and Bony (knee) have both been ruled out for the rest of the season.
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The spate of injuries is a blow to 17th-placed Swansea as they battle to stay in the top flight. The Welsh club take on seventh-placed Burnley in the league on Saturday.
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Amlan Chakraborty)
