Washington quarterback Alex Smith is battling an infection and may still be in hospital after a serious leg injury he sustained last month, according to multiple reports.

Smith underwent surgery after he broke his tibia and fibula on 18 November against the Houston Texans. Reports first emerged on Wednesday that the 34-year-old is still in hospital after suffering an infection following the surgery and NFL.com’s Ian Rapoport followed up the story on Thursday. “Alex Smith is battling an infection related to the surgery he had on his broken fibula and tibia, sources say,” he wrote on Twitter. “It’s premature to say what this means for his playing future. But it is being handled with care and dealt with seriously by doctors.” Rapoport did not say whether Smith is still in hospital.

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Washington issued a statement on Thursday but did not comment on the reports of an infection. “On behalf of Alex Smith, we appreciate all of the concerns and prayers over the injury he incurred on November 18th against the Houston Texans,” the team wrote in a statement. “Although this is a serious injury, Alex and his family remain strong. We would ask that everyone please honor the Smith family’s request for privacy at this time.”

Ian Rapoport (@RapSheet) #Redskins QB Alex Smith is battling an infection related to the surgery he had on his broken fibula and tibia, sources say. It’s premature to say what this means for his playing future. But it is being handled with care and dealt with seriously by doctors.

Washington looked set for a playoff place until Smith’s injury but have lost all three of their games in his absence. His replacement, Colt McCoy, sustained a season-ending injury of his own against the Philadelphia Eagles on Monday. Washington must now rely on Mark Sanchez and Josh Johnson, neither of whom has played regularly in the NFL for a number of years, for the rest of the season.