"He's moving around and well on his way to a recovery," Allen told reporters Tuesday, according to Jeremy Bergman of NFL.com. "It's a tough thing for him and his family. All the love and care has helped him quite a bit.
"We'll see how it goes. We're optimistic. If anyone can come back, it's Alex. I'm sure he wanted to shoot hoops at the game yesterday, but we'll see."
Smith made his first public appearance since the injury when he attended Monday's Washington Wizards game, and he was still sporting a significant brace on his right leg.
Smith started the first 10 games of the season following last year's trade from the Kansas City Chiefs before suffering a broken leg against the Houston Texans in Week 11.
The 34-year-old led the team to a 6-4 record before the injury. He completed 62.5 percent of his passes for 2,180 yards and 10 touchdowns against five interceptions and added 168 yards and a score as a rusher.
Smith was replaced under center by Colt McCoy, who later suffered a leg injury of his own. Veteran journeymen Mark Sanchez and Josh Johnson closed out the campaign at quarterback as the Redskins finished at 7-9 and third in the NFC East.
Allen wouldn't say whether the team plans to address the depth at the position this offseason.
"We prioritize every position on the team," Allen added. "And we'll see what we get in free agency and the draft."