Sources told ESPN's Dianna Russini that there is concern that Smith, 34, is dealing with a career-ending injury after breaking the tibia and fibula in his right leg during a Week 11 loss to the Houston Texans on Nov. 18.
Smith remains in the hospital, where he has been since suffering the injury on Nov. 18, sources told Russini.
The Redskins released a statement addressing Smith's health on Thursday, saying they were requesting privacy for Smith and his family amid his recovery.
"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 statement said. "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."
Burgundy Blog, a Redskins-focused website, first reported the complications related to Smith's recovery.
Redskins coach Jay Gruden said last week that he had met with Smith, noting the quarterback was continuing to rehab.
"It's a tough road, and any time you have surgery on your leg, it's not easy, but he's got a great support system, great doctors, and hopefully he'll recover fast," Gruden said Nov. 29.