"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."
Allen did not say whether Washington is looking to add another quarterback.
"We prioritize every position on the team," Allen added. "And we'll see what we get in free agency and the draft."
Allen could not confirm whether Smith needed more surgeries, saying, "I'm not going to get into that and I'm not a doctor. ... He's going to follow the doctor's advice and his wife's advice and well see what happens."
The Redskins quarterback suffered a season-ending compound leg fracture in Week 11 and underwent multiple surgeries soon after. He was released from the hospital in mid-December following a leg infection. Smith showed up at a Washington Wizards game on Monday wearing an apparatus on his right leg and was seen wearing crutches in the locker room.
NFL Network Insider Ian Rapoport reported Tuesday that Smith's recovery has gone "as well as it could be hoped", but it is a "supreme long shot" that Smith will start the 2019 season under center in D.C. "if he is going to play at all."
Washington's big offseason signing in 2018, Smith is entering the first season of a four-year extension signed with the 'Skins after they acquired him from the Kansas City Chiefs. Smith carries a cap number of $20.4 million in 2019, the highest on the team.