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.
Smith remains in the hospital, where he has been since suffering the injury Nov. 18, sources told Russini. Running back Adrian Peterson said Thursday that Redskins players visited Smith in the hospital last week.
"I'll continue to pray for him. We had the opportunity to see him last week. We all just [assured] him we're praying for you, man, and wishing the best for him. That's all we can do," he said.
Cornerback Josh Norman said Smith is a "strong man."
"I know he's handling it and just going through the process. ... I reached out to him a couple times, go by and see him a little bit. I know it's rough right now for us to get out that way. ... He said a couple things to the team; that's pretty cool. That was welcoming. He's definitely in good hands; praying for him, one of our fallen brothers, we're definitely praying for him. We're uplifting him every way we can and that's all you can ask for," he said.
"He's the most resilient man I ever met. An injury like this, I'm sure he'll work through it. He'll get through it. He's optimistic about everything. If I know him, I know how he'll handle everything. I'll just keep him in my prayers and hope for the best," Davis said.
The Redskins released a statement Thursday addressing Smith's health, 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.
ESPN's John Keim contributed to this report.